[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12448#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12448","headline":"\u8fd1\u4f3c – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u8fd1\u4f3c – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u8fd1\u4f3c \uff08\u6ce8\u3050\u3002 \u8fd1\u4f3c – \u8fd1\u3065\u304f\uff09 – \u304a\u304a\u3088\u305d\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306e\u69cb\u7bc9\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7279\u5b9a\u306e\u65b9\u6cd5\u3067\u3001\u5206\u6790\u5f62\u5f0f\u3067\u6b63\u78ba\u306b\u63d0\u793a\u3067\u304d\u306a\u3044\u554f\u984c\u306b\u5bfe\u3059\u308b\u53b3\u683c\u306a\u89e3\u6c7a\u7b56 [\u521d\u3081] \u3002\u6700\u3082\u4e00\u822c\u7684\u306a\u8fd1\u4f3c\u306f\u3001\u7279\u5b9a\u306e\u95a2\u6570\u3092\u63d0\u793a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} after-content-x4 \u5225\u306e\u3001\u901a\u5e38\u3088\u308a\u30b7\u30f3\u30d7\u30eb\u306a\u5f62\u3067 \u30d5\u30a1\u30a4 \uff08","datePublished":"2020-03-11","dateModified":"2020-03-11","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/202945cce41ecebb6f643f31d119c514bec7a074","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/202945cce41ecebb6f643f31d119c514bec7a074","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12448","wordCount":17933,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u8fd1\u4f3c \uff08\u6ce8\u3050\u3002 \u8fd1\u4f3c  – \u8fd1\u3065\u304f\uff09 – \u304a\u304a\u3088\u305d\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306e\u69cb\u7bc9\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7279\u5b9a\u306e\u65b9\u6cd5\u3067\u3001\u5206\u6790\u5f62\u5f0f\u3067\u6b63\u78ba\u306b\u63d0\u793a\u3067\u304d\u306a\u3044\u554f\u984c\u306b\u5bfe\u3059\u308b\u53b3\u683c\u306a\u89e3\u6c7a\u7b56 [\u521d\u3081] \u3002\u6700\u3082\u4e00\u822c\u7684\u306a\u8fd1\u4f3c\u306f\u3001\u7279\u5b9a\u306e\u95a2\u6570\u3092\u63d0\u793a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5225\u306e\u3001\u901a\u5e38\u3088\u308a\u30b7\u30f3\u30d7\u30eb\u306a\u5f62\u3067 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle varphi\uff08x\uff09\u3001} \u554f\u984c\u306b\u5bfe\u3059\u308b\u52b9\u679c\u7684\u306a\u89e3\u6c7a\u7b56\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u79c1\u305f\u3061\u304c\u6271\u3063\u3066\u3044\u308b\u3053\u306e\u3088\u3046\u306a\u72b6\u6cc1 \u3057\u3063\u304b\u308a\u3068\u30de\u30fc\u30b8\u3067\u304d\u306a\u3044\u95a2\u6570\u3067\u30de\u30fc\u30af\u3055\u308c\u305f\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001 \u901a\u5e38\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u90e8\u5206\u7684\u306a\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u304d\u3001\u4e0d\u660e\u306a\u95a2\u6570\u3092\u63a2\u3059\u3068\u304d\u3001 \u6e2c\u5b9a\u3092\u958b\u767a\u3059\u308b\u5834\u5408\u3001\u63a7\u3048\u3081\u306a\u30bb\u30c3\u30c8\u30bb\u30c3\u30c8\u3067\u306e\u307f\u77e5\u3089\u308c\u3066\u3044\u308b\u7d50\u679c\uff08\u6c17\u8c61\u5b66\u306a\u3069\uff09\u3002 \u8fd1\u4f3c\u306f\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3067\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u53b3\u5bc6\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u610f\u5473\u3067O\u6700\u9069\u306a\u8fd1\u4f3c\u3092\u63a2\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4e00\u822c\u306b\u3001\u8fd1\u4f3c\u306f\u7279\u5b9a\u306e\u95a2\u6570\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle f\uff08x\uff09\u3001} \u30a8\u30ea\u30a2\u5185 \u304a\u304a {displaystyle omega} \u7570\u306a\u308b\u3001\u3088\u308a\u30b7\u30f3\u30d7\u30eb\u306a\u8fd1\u4f3c\u95a2\u6570\u3092\u5099\u3048\u305f\u305d\u306e\u6c7a\u5b9a \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle varphi\uff08x\uff09\u3001} \u5024\u304c\u591a\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u4f9d\u5b58\u3059\u308b\u306e\u3068\u540c\u3058\u9818\u57df\u3067\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u95a2\u6570\u3068\u3057\u3066        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle varphi\uff08x\uff09\u3001} \u4e00\u822c\u7684\u306b\u4e00\u822c\u5316\u3055\u308c\u305f\u591a\u9805\u5f0f\u306f\u3001\u5f62\u5f0f\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059 \u03c6(x)=a1\u03c61(x)+a2\u03c62(x)+\u2026+an\u03c6n(x),{displaystyle varphi (x)=a_{1}varphi _{1}(x)+a_{2}varphi _{2}(x)+,dots ,+a_{n}varphi _{n}(x),} \uff08a\uff09 \u3069\u306e\u6a5f\u80fd \u30d5\u30a1\u30a4 \u79c1 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle varphi _ {i}\uff08x\uff09} \u5f7c\u3089\u306fSO -Called\u3092\u5f62\u6210\u3057\u307e\u3059 \u8fd1\u4f3c\u30d9\u30fc\u30b9  b \uff08 \u30d0\u30c4 \uff09\uff09 = [ \u30d5\u30a1\u30a4 1\uff08 \u30d0\u30c4 \uff09\uff09 \u3001 \u30d5\u30a1\u30a4 2\uff08 \u30d0\u30c4 \uff09\uff09 \u3001 … \u30d5\u30a1\u30a4 n\uff08 \u30d0\u30c4 \uff09\uff09 ] \u3001 {displaystyle mathbf {b}\uff08x\uff09= [varphi _ {1}\uff08x\uff09,, varphi _ {2}\uff08x\uff09,, dots\u3001varphi _ {n {n}\uff08x\uff09\u3001} \u3068 a \u79c1 {displaystyle a_ {i}} \u305d\u308c\u3089\u306f\u6570\u5024\u3067\u3059 \u5ea7\u6a19 \u95a2\u6570 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle varphi\uff08x\uff09} \u63a1\u7528\u3055\u308c\u305f\u30d9\u30fc\u30b9\u306b\u5bfe\u3057\u3066\u3002\u3053\u308c\u3089\u306e\u4fc2\u6570\u306e\u9078\u629e\u306f\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3067\u884c\u308f\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u8fd1\u4f3c\u8aa4\u5dee\u304c\u53ef\u80fd\u306a\u9650\u308a\u4f4e\u304f\u306a\u308b\u3088\u3046\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u610f\u5473\u3067\u8fd1\u4f3c\u3092\u69cb\u7bc9\u3059\u308b\u5b9f\u7528\u7684\u306a\u65b9\u6cd5\u306e1\u3064\u306f\u3001\u95a2\u6570\u306e\u9055\u3044\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3067\u6307\u5b9a\u3055\u308c\u305f\u8fd1\u4f3c\u8aa4\u5dee\u3092\u6700\u5c0f\u5316\u3059\u308b\u65b9\u6cd5\u3067\u3059 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle varphi\uff08x\uff09,, f\uff08x\uff09}  R(a1,a2,\u2026an)=\u27e8[\u03c6(x)\u2212f(x)]\u22c5[\u03c6(x)\u2212f(x)]\u27e9=\u27e8[\u03c6(x)\u2212f(x)]2\u27e9,{displaystyle R(a_{1},,a_{2},,dots ,a_{n})={big langle }[varphi (x)-f(x)]cdot [varphi (x)-f(x)]{big rangle }={big langle }[varphi (x)-f(x)]^{2}{big rangle },} \uff08b\uff09 \u3053\u306e\u88fd\u54c1\u306f\u30012\u3064\u306e\u65b9\u6cd5\u3067\u5b9a\u7fa9\u3067\u304d\u307e\u3059 [2] \uff1a \u27e8g\u22c5h\u27e9=\u222b\u03a9g(x)h(x)d\u03a9{displaystyle langle gcdot hrangle =int _{Omega }g(x)h(x)dOmega quad {}} \u27e8g\u22c5h\u27e9=\u2211i=1ng(xi)h(xi),xi\u2208\u03a9.{displaystyle {}quad langle gcdot hrangle =sum _{i=1}^{n}g(x_{i})h(x_{i}),;;x_{i}in Omega .} \uff08c\uff09 \u3053\u306e\u3088\u3046\u306a\u7279\u5b9a\u306e\u30a8\u30e9\u30fc\u3092\u6700\u5c0f\u5316\u3059\u308b\u306b\u306f\u3001\u305d\u308c\u304c\u5fc5\u8981\u3067\u3059 12\u2202R\u2202ak=\u2202\u2202ak\u27e8(\u03c6\u2212f)2\u27e9=\u27e8(\u03c6\u2212f)\u22c5\u2202\u2202ak\u03c6\u27e9=\u27e8(\u03c6\u2212f)\u22c5\u03c6k\u27e9=\u27e8\u03c6\u22c5\u03c6k\u27e9\u2212\u27e8f\u22c5\u03c6k\u27e9=\u2211i=1n\u27e8\u03c6k\u22c5\u03c6i\u27e9ai\u2212\u27e8\u03c6k\u22c5f\u27e9=0,k=1,2,\u2026n.{displaystyle {begin{aligned}{tfrac {1}{2}}{tfrac {partial R}{partial a_{k}}}&={tfrac {partial }{partial a_{k}}}langle (varphi -f)^{2}rangle \\&={big langle }(varphi -f)cdot {tfrac {partial }{partial a_{k}}}varphi {big rangle }\\&={big langle }(varphi -f)cdot varphi _{k}{big rangle }\\&=langle varphi cdot varphi _{k}rangle -langle fcdot varphi _{k}rangle \\&=sum _{i=1}^{n}langle varphi _{k}cdot varphi _{i}rangle a_{i}-langle varphi _{k}cdot frangle =0,quad k=1,,2,,dots ,n.end{aligned}}} \uff08d\uff09 \u4e0a\u8a18\u306e\u95a2\u6570\u306e\u8fd1\u4f3c\u65b9\u6cd5 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} \u591a\u9805\u5f0f\u306e\u4f7f\u7528 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle varphi\uff08x\uff09} \u30d1\u30bf\u30fc\u30f3\uff08b\uff09\u3067\u6307\u5b9a\u3055\u308c\u305f\u30a8\u30e9\u30fc\u3092\u6700\u5c0f\u5316\u3059\u308b\u305f\u3081\u306b\u3001\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u7b56\u5b9a\u304a\u3088\u3073\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u6761\u4ef6\u306f\u3001\u5f0f\uff08d\uff09\u306e\u30b7\u30b9\u30c6\u30e0\u306e\u5f62\u3092\u53d6\u308a\u307e\u3057\u305f\u3002 a \u79c1 {displaystyle a_ {i}} \u305d\u308c\u3089\u306f\u6a5f\u80fd\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3057\u305f \u27e8 \u30d5\u30a1\u30a4 k de \u30d5\u30a1\u30a4 \u79c1 \u27e9 \u3001 \u27e8 \u30d5\u30a1\u30a4 k de f \u27e9 {displaystyle langle varphi _ {k} cdot varphi _ {i} rank\u3001; langle varphi _ {k} cdot frangle} \u95a2\u6570\u306e\u305f\u3081 \u30d5\u30a1\u30a4 k \u3002 {displaystyle varphi _ {k}\u3002}  \u7dda\u5f62\u7a7a\u9593\u3067\u306e\u8fd1\u4f3c\u306e\u4e00\u822c\u7684\u306a\u5b9a\u5f0f\u5316 f {displaystyle f} \u3053\u306e\u8fd1\u4f3c\u304c\u6e80\u305f\u3059\u3053\u3068\u3067\u3042\u308b\u6761\u4ef6\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 by F\u00af{displaystyle {bar {f}}} \u30b5\u30d6\u30bb\u30c3\u30c8\u3092\u30de\u30fc\u30af\u3057\u307e\u3059 \uff08 F\u00af\u2282 f \uff09\uff09 {displaystyle\uff08{bar {f}}\u30b5\u30d6\u30bb\u30c3\u30c8f\uff09} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3 f \u3001 {displaystyle f\u3001} \u307e\u305f\u3001\u3053\u308c\u306f\u7dda\u5f62\u7a7a\u9593\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u8fd1\u4f3c\u306f\u3059\u3079\u3066\u306e\u8981\u7d20\u306b\u5bfe\u3057\u3066\u69cb\u6210\u3055\u308c\u307e\u3059 f \u2208 f {displaystyle fin f} \u305d\u306e\u3088\u3046\u306a\u8981\u7d20\u3092\u898b\u3064\u3051\u307e\u3059 f\u00af\u2208 F\u00af\u3001 {displaystyle {bar {f}} in {bar {f}}\u3001} \u3069\u306e\u5e73\u7b49\u304c\u8d77\u3053\u308b\u304b l k\uff08 f\u00af\uff09\uff09 = l k\uff08 f \uff09\uff09 \u3001 {displaystyle l_ {k}\uff08{bar {f}}\uff09= l_ {k}\uff08f\uff09\u3001quad {}} \u305f\u3081\u306b k = \u521d\u3081 \u3001 2 \u3001 … n \u3001 {displaystyle {} quad k = 1\u3001\u30012\u3001\u3001dots\u3001n\u3001} \u305d\u306e\u4e2d\u3067 l k {displaystyle l_ {k}} \u7279\u5b9a\u306e\u7dda\u5f62\u95a2\u6570\u3067\u3059\u3001 \u8fd1\u4f3c\u306e\u6761\u4ef6\u3092\u6c7a\u5b9a\u3057\u307e\u3059 \u3002 \u3057\u305f\u304c\u3063\u3066\u3001\u8fd1\u4f3c\u306e\u554f\u984c\u306b\u306f\u30013\u3064\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u5b9a\u7fa9\u304c\u5fc5\u8981\u3067\u3059\u3002 \u95a2\u6570 F,{displaystyle f\u3001} \u8fd1\u4f3c\u95a2\u6570\u3001 \u95a2\u6570 F\u00af,{displaystyle {bar {f}}\u3001} \u95a2\u6570\u306e\u8fd1\u4f3c\u3001 \u9806\u5e8f l1,l2,\u2026ln{displaystyle l_ {1} ,, l_ {2} ,, dots\u3001l_ {n}}}}} \u7dda\u5f62\u95a2\u6570\u3002 \u307b\u3068\u3093\u3069\u306e\u5834\u5408 F\u00af\u3001 {displaystyle {bar {f}}\u3001} \u30ad\u30e3\u30e9\u30af\u30bf\u30fc\u306b\u95a2\u3059\u308b\u4e00\u822c\u7684\u306a\u591a\u9805\u5f0f\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u304c\u9078\u3070\u308c\u307e\u3059 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 = \u2211 i=1na i\u30d5\u30a1\u30a4 i\uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle varphi\uff08x\uff09= sum _ {i = 1} ^^ {n _ {i} varphi _ _ _ _\uff08x\uff09} \u30d9\u30fc\u30b9\u95a2\u6570\u304b\u3089\u4f5c\u6210\u3055\u308c\u307e\u3057\u305f \u30d5\u30a1\u30a4 \u521d\u3081 \u3001 \u30d5\u30a1\u30a4 2 \u3001 … \u30d5\u30a1\u30a4 n \u2208 f \u3002 {displaystyle varphi _ {1} ,, varphi _ {2} \u3053\u306e\u5834\u5408 F\u00af{displaystyle {bar {f}}} \u305d\u308c\u306fN\u6b21\u5143\u306e\u4e0b\u5c64\u571f\u306b\u306a\u308a\u307e\u3059 f \u3002 {displaystyle F.}  \u8981\u7d20\u306e\u691c\u7d22 f\u00af\u2208 F\u00af\u3001 {displaystyle {bar {f}} in {bar {f}}\u3001} \u8fd1\u4f3c f \u2208 f {displaystyle fin f} \u3053\u308c\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u591a\u9805\u5f0f\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3067\u3059 \u30d5\u30a1\u30a4 \u2208 F\u00af{{bar {f}}}\u306edisplaystyle varphi  \u03c6=a1\u03c61+a2\u03c62+\u2026+an\u03c6n,{displaystyle varphi =a_{1}varphi _{1}+a_{2}varphi _{2}+,dots ,+a_{n}varphi _{n},} \uff08\u305d\u3046\u3067\u3059\uff09 \u5e73\u7b49\u3092\u6e80\u305f\u3057\u3066\u3044\u307e\u3059  lk(\u03c6)=\u2211i=1nlk(\u03c6i)ai=lk(f),k=1,2,\u2026n.{displaystyle l_ {k}\uff08varphi\uff09= sum _ {i = 1}^{n} l_ {k}\uff08varphi _ _ _ _ _ _ _ = l_ {k}\uff08f\uff09\u3001quad k = 1\u30012\u3001dots\u3001n\u3002}}  \uff08f\uff09 \u7dda\u5f62\u7d50\u5408\u306e\u4fc2\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u65b9\u7a0b\u5f0f\u306e\u30b7\u30b9\u30c6\u30e0\u3092\u4f5c\u6210\u3057\u307e\u3059\uff08E\uff09\u3002 \u306e\u5834\u5408 \u30d5\u30a1\u30a4 \u79c1 \uff08 \u30d0\u30c4 \uff09\uff09 \u2208 f {displaystyle varphi _ {i}\uff08x\uff09in f} \u76f4\u7dda\u7684\u306b\u72ec\u7acb\u3057\u305f\u95a2\u6570\u3092\u63a1\u7528\u3057\u307e\u3059\u3002\u65b9\u7a0b\u5f0f\u30b7\u30b9\u30c6\u30e0\u306e\u3053\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u3001\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u975e\u5e38\u306b\u3044\u3063\u3071\u3044\u3067\u3059\u3002\u307e\u308c\u306a\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u3088\u3063\u3066\u7279\u5fb4\u4ed8\u3051\u3089\u308c\u308b\u3053\u306e\u3088\u3046\u306a\u65b9\u7a0b\u5f0f\u306e\u30b7\u30b9\u30c6\u30e0\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u306b\u3001\u6b21\u306e\u8fd1\u4f3c\u3092\u69cb\u7bc9\u3057\u3066\u3044\u307e\u3059 f\u00af\u2208 F\u00af{displaystyle {bar {f}} in {bar {f}}}  \u88dc\u9593\u306e\u305f\u3081\u306b\u72ed\u304f\u306a\u3063\u305f [3] \u3001\u6b21\u306e\u5f62\u5f0f\u3067 f\u00af=c1\u03d51(x)+c2\u03d52(x)+\u2026cn\u03d5n(x),{displaystyle {bar {f}}=c_{1}phi _{1}(x)+c_{2}phi _{2}(x)+,dots ,c_{n}phi _{n}(x),} \uff08g\uff09 \u3053\u306e\u3088\u3046\u306a\u8fd1\u4f3c\u306e\u30d9\u30fc\u30b9\u306f\u95a2\u6570\u3067\u3059 \u03d5 \u79c1 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle phi _ {i}\uff08x\uff09} \u3053\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u3064\u3044\u3066 l k \u03d5 \u79c1 = d k \u79c1 \u3002 {displaystyle l_ {k} phi _ {i} = delta _ {ki}\u3002} \u3057\u305f\u304c\u3063\u3066\u3001 lkf\u00af=lk(\u2211i=1nci\u03d5i)=\u2211i=1ncilk\u03d5i=ck{displaystyle l_ {k {k}} quad {}} \u3068 f\u00af=\u2211k=1n(lkf\u00af)\u03d5k.mm\u30b9\u30ec\u30fc\u30d3\u30fc  \uff08h\uff09 \u6a5f\u80fd \u03d5 s \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 s = \u521d\u3081 \u3001 2 \u3001 … n {displaystyle phi _ {s}\uff08x\uff09\u3001; s = 1 ,, 2 ,\u3001\u30c9\u30c3\u30c8\u3001n} \u7d44\u307f\u5408\u308f\u305b\u306b\u57fa\u3065\u3044\u3066\u53d6\u5f97\u3055\u308c\u307e\u3059\uff08e\uff09 \u03d5 s\uff08 \u30d0\u30c4 \uff09\uff09 = \u2211 k=1na i(s)\u30d5\u30a1\u30a4 s\uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle phi _ {s}\uff08x\uff09= sum _ {k = 1}^{n _ a_ {i}^{\uff08s\uff09} varphi _ {s}\uff08x\uff09\u3001} \u305d\u306e\u4fc2\u6570 a \u79c1 \uff08 s \uff09\uff09 {displaystyle a_ {i}^{\uff08s\uff09}} \u95a2\u6570\u304c\u3042\u308b\u65b9\u7a0b\u5f0f\uff08f\uff09\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} \u5f8c\u7d9a\u306e\u95a2\u6570\u306b\u7f6e\u304d\u63db\u3048\u3089\u308c\u307e\u3059 \u03d5 s \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 s = \u521d\u3081 \u3001 2 \u3001 … n \u3002 {displaystyle phi _ {s}\uff08x\uff09\u3001; s = 1 ,, 2 ,\u3001\u30c9\u30c3\u30c8\u3001n\u3002} \u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u30d9\u30fc\u30b9\u95a2\u6570\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u6a5f\u80fd f \uff08 \u30d0\u30c4 \uff09\uff09 = \u30d0\u30c4 2 {displaystyle f\uff08x\uff09= x^{2}} \u7bc4\u56f2\u3067\u8fd1\u4f3c\u3067\u304d\u307e\u3059 \uff08 0 \u3001 \u521d\u3081 \uff09\uff09 \u2208 r \u521d\u3081 \u3001 {displaystyle\uff080\u3001\u30011\uff09in r^{1}\u3001} \u305d\u308c\u3092\u4eee\u5b9a\u3057\u305f\u7dda\u5f62\u95a2\u6570 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 = a 1\u30d5\u30a1\u30a4 1\uff08 \u30d0\u30c4 \uff09\uff09 + a 2\u30d5\u30a1\u30a4 2\uff08 \u30d0\u30c4 \uff09\uff09 = a 1+ a 2\u30d0\u30c4 {displaystyle varphi\uff08x\uff09= a_ {1} varphi _ {1}\uff08x\uff09+a_ {2} varphi _ {2}\uff08x\uff09= a_ {1}+a_ {2} x} \u305f\u3068\u3048\u3070\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306e\u5f62\u30672\u3064\u306e\u6a5f\u80fd\u3092\u5b9a\u7fa9\u3059\u308b l k\uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = \u27e8 \u30d5\u30a1\u30a4 kde \u30d5\u30a1\u30a4 \u27e9 = \u222b 01\u30d5\u30a1\u30a4 k\uff08 \u30d0\u30c4 \uff09\uff09 de \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 \u3001 k = \u521d\u3081 \u3001 2\u3002 {displaystyle l_ {k}\uff08varphi\uff09= langle varphi _ {k} cdot varphi rangle = int _ {0}^{1} !! varphi _ _ _ _ _ _\uff09 \u6761\u4ef6\uff08f\uff09\u30d5\u30a9\u30fc\u30e0\u3092\u53d6\u5f97\u3057\u307e\u3059 \u27e8 \u30d5\u30a1\u30a4 kde \u30d5\u30a1\u30a4 1\u27e9 a 1+ \u27e8 \u30d5\u30a1\u30a4 kde \u30d5\u30a1\u30a4 2\u27e9 a 2= \u27e8 \u30d5\u30a1\u30a4 kde f \u27e9 \u3001 k = \u521d\u3081 \u3001 2\u3002 {displaystyle langle varphi _ {k} cdot varphi _ {1} rangle a_ {1}+langle varphi _ {k} cdot varphi _ {2 {2 {2} {2} = langle varphi _ {k} \u4fc2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059 a \u521d\u3081 \u3001 a 2 {displaystyle a_ {1} ,, a_ {2}} \u65b9\u7a0b\u5f0f\u306e\u30b7\u30b9\u30c6\u30e0\u304c\u53d6\u5f97\u3055\u308c\u307e\u3059 [1121213][a1a2]= [1314]\u2192 a 1=  –  16\u3001 a 2= \u521d\u3081\u3002 {displaystyle {begin {bmatrix} 1\uff06{tfrac {1} {2}} \\ {tfrac {1} {2}}\uff06{tfrac {1} {3}} end {bmatrix}}} {{bmatrix} {bmatrix} {bmatrix} {bmatrix} {bmatrix} {bmatrix} }} = {begin {bmatrix} {tfrac {1} {3}} \\ {tfrac {1} {4} {4}} end {bmatrix}} Quad to Quad a_ {1} =  –  {tfrac {1}} {6}} \u95a2\u6570\u306e\u627f\u8a8d f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} \u7bc4\u56f2\u3067\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059 [ a \u3001 b ] {displaystyle [a ,, b]} \u95a2\u6570\u306e\u8fd1\u4f3c\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 \uff08 \u30d0\u30c4 = b+a2+ b\u2212a2\u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08xi\uff09\u3001;\uff08x = {tfrac {b+a} {2}}+{tfrac {b-a} {2}} xi\uff09}} \u6a19\u6e96\u7bc4\u56f2 [  –  \u521d\u3081 \u3001 \u521d\u3081 ] \u3002 {displaystyle [-1 ,, 1]\u3002} \u4e00\u822c\u5316\u3055\u308c\u305f\u7a0b\u5ea6\u306e\u591a\u9805\u5f0f\u306e\u5f62\u3067\u8fd1\u4f3c\u30d9\u30fc\u30b9\u3092\u69cb\u7bc9\u3057\u307e\u3059 n {displaystyle n}  \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 = a 0\u306e 0\uff08 \u30d0\u30c4 \uff09\uff09 + a 1\u306e 1\uff08 \u30d0\u30c4 \uff09\uff09 + … + a n\u306e n\uff08 \u30d0\u30c4 \uff09\uff09 \u3001 {displaystyle varphi\uff08xi\uff09= a_ {0} w_ {0}\uff08xi\uff09+a_ {1} w_ {1}\uff08xi\uff09+\u3001dods\u3001+a_ {n} w_ {n}\uff08xi\uff09\u3001} \u4efb\u610f\u306e\u95a2\u6570\u304b\u3089\u5f62\u6210\u3055\u308c\u307e\u3059\u304c\u3001\u76f4\u4ea4\u3059\u308b\u76f8\u4e92\u306b\u3001\u6a19\u6e96\u7bc4\u56f2\u3067\u5145\u5b9f\u3057\u305f\u6761\u4ef6\u3067\u5145\u5b9f\u3057\u3066\u3044\u307e\u3059 \u222b \u221211\u306e k\uff08 \u30d0\u30c4 \uff09\uff09 \u306e i\uff08 \u30d0\u30c4 \uff09\uff09 d \u30d0\u30c4 = 0 \u3001 {displaystyle int _ {-1}^{1} !! w_ {k}\uff08xi\uff09w_ {i}\uff08xi\uff09dxi = 0\u3001quad {}}}} \u3044\u3064 \u79c1 \u2260 k \u3002 {displaysStyle {}; ineq K.} \u6a5f\u80fd\u3057\u307e\u3057\u305f l k \u3001 {displaystyle l_ {k}\u3001} \u79c1\u305f\u3061\u306f\u5f62\u3067\uff08f\uff09\u306b\u53d7\u3051\u5165\u308c\u307e\u3059 l k\uff08 f \uff09\uff09 = \u27e8 \u306e kde f \u27e9 = \u222b \u221211\u306e k\uff08 \u30d0\u30c4 \uff09\uff09 f \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 k = 0 \u3001 \u521d\u3081 \u3001 … n \u3002 {displaystyle l_ {k}\uff08f\uff09= langle w_ {k} cdot frangle = int _ {-1}^{1} w_ {k}\uff08xi\uff09f\uff08xi\uff09\u3001quad k = 0 \u3001\u3001 1\u3001dots\u3001n\u3002}} \u79c1\u305f\u3061\u3082\u6301\u3063\u3066\u3044\u307e\u3059 lk(\u03c6)=\u27e8wk\u22c5\u03c6\u27e9=\u222b\u221211wk(\u03be)\u03c6(\u03be)=\u222b\u221211wk(\u03be)\u2211i=1naiwi(\u03be)d\u03be=\u222b\u221211akwk2(\u03be)d(\u03be)=\u27e8wk\u22c5wk\u27e9ak,k=0,1,\u2026n.{displaystyle {begin {aligned} l_ {k}\uff08varphi\uff09\uff06= langle w_ {k} cdot varphi rangle \\\uff06= int _ { –  1}^{1} w_ {k}\uff08xi\uff09varphi\uff08xi\uff09\\\uff06= int _ {1}^{1}^{1} {x} }^{n} a_ {i} w_ {i}\uff08xi\uff09dxi \\\uff06= int _ { –  1}^{1} !! a_ {k} w_ {k}^{2}\uff08xi\uff09d\uff08xi\uff09\\\uff06= langle w_ {k} .end {aligned}}} \u65b9\u7a0b\u5f0f\u30b7\u30b9\u30c6\u30e0\uff08f\uff09\u306f\u6700\u3082\u5358\u7d14\u306a\u5f62\u5f0f\u306b\u7e2e\u5c0f\u3055\u308c\u307e\u3059 \u27e8 \u306e kde f \u27e9 = \u27e8 \u306e kde \u306e k\u27e9 a k\u2192 a k= \u27e8wk\u22c5F\u27e9\u27e8wk\u22c5wk\u27e9\u3001 k = 0 \u3001 \u521d\u3081 \u3001 … n \u3002 {displaystyle langle w_ {k} cdot frangle = langle w_ {k} cdot w_ {k} rangle a_ {k} quad to quad a_ {k} = {tfrac {langle w_ {k} cdot frangle} {langle w_ {k} cdot w_ {k} \u6a5f\u80fd\u3057\u307e\u3057\u305f \u27e8 \u306e k de \u306e k \u27e9 \u3001 k = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … n {displaystyle langle w_ {k} cdot w_ {k} rangle\u3001; k = 0\u30011 ,\u30012 ,\u3001\u30c9\u30c3\u30c8\u3001n} \u305f\u3068\u3048\u3070\u3001\u5024\u304c\u3042\u308a\u307e\u3059 \u27e8wk\u22c5wk\u27e9=22k+1,{displaystyle langle w_ {k} cdot w_ {k} rangle = {tfrac {2} {2k+1}}\u3001quad {}} \u6a5f\u80fd\u3059\u308b\u5834\u5408 wk(x){displaystyle w_ {k}\uff08x\uff09} \u5f7c\u3089\u306f\u4f1d\u8aac\u7684\u306a\u591a\u9805\u5f0f\u3067\u3059 [2] \u7a0b\u5ea6 k,{displaystyle k\u3001} \u27e8wk\u22c5wk\u27e9=1,{displaystyle\u30e9\u30f3\u30b0\u30ebw_ {k} cdot w_ {k} rangle = 1\u3001quad {}} \u3044\u3064 w0(\u03be)=12,wk(\u03be)=cos\u2061(k\u03c0\u03be),k=1,2,\u2026,n,{displaystyle {}; w_ {0}\uff08xi\uff09= {tfrac {1} {sqrt {2}}}\u3001;; w_ {k}\uff08xi\uff09= cos\uff08kpi xi\uff09; \u27e8w0\u22c5w0\u27e9=\u03c0,\u27e8wk\u22c5wk\u27e9=\u03c02,k=1,2,\u2026n,{displaystyle langle w_ {0} cdot w_ {0} rangle = pi\u3001;; langle w_ {k} cdot w_ {k} rangle = {tfrac {pi} {2}} \u6a5f\u80fd\u3059\u308b\u5834\u5408 wk(x){displaystyle w_ {k}\uff08x\uff09} \u305d\u308c\u3089\u306fCzebyszew\u306e\u591a\u9805\u5f0f\u3067\u3059 [2] \u7a0b\u5ea6 k.{displaystyle k\u3002} \u6700\u826f\u306e\u8fd1\u4f3c\u3092\u5b9a\u7fa9\u3057\u307e\u3059 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u898f\u5236\u30b9\u30da\u30fc\u30b9\u3067 \u7dda\u5f62\u7a7a\u9593\u3092\u4e0e\u3048\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u6a19\u6e96\u3067 \u2016 de \u2016 {displaystyle | cdot |} \u3068\u3055\u305b\u3066\u304f\u3060\u3055\u3044 \u306e \u2282 \u30d0\u30c4 {displaystyle vsubset x} \u305d\u308c\u306f\u7dda\u5f62\u90ca\u5916\u306b\u306a\u308a\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u5b8c\u6210\u3057\u305f\u5bf8\u6cd5\u3002\u6700\u826f\u306e\u8fd1\u4f3c\u306e\u30bf\u30b9\u30af\u306f\u305d\u306e\u3088\u3046\u306a\u3082\u306e\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059 \u306e \u2217 \u2208 \u306e {displaystyle v^{*} in v} \uff08\u4e0e\u3048\u3089\u308c\u305f\u6700\u826f\u306e\u8fd1\u4f3c\u306e\u8981\u7d20 \u30d0\u30c4 \u2208 \u30d0\u30c4 {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \uff09\u305d\u308c\u306f\u3042\u308a\u307e\u3059\uff1a \u2200 \u306e \u2208 \u306e \u2016 \u30d0\u30c4  –  \u306e \u2217\u2016 \u2a7d \u2016 \u30d0\u30c4  –  \u306e \u2016 {displaystyle forall {vin v} quad | x-v^{*} | leqslant | x-v |} \u8981\u7d20\u304c\u7406\u89e3\u3055\u308c\u308b\u3079\u304d\u3067\u3059 \u306e \u2217 {displaystyle v^{*}} \u8fd1\u4f3c\u306b\u300c\u6700\u3082\u8fd1\u3044\u300d\u8981\u7d20\u3067\u3059 \u30d0\u30c4 {displaystyle x} \u3059\u3079\u3066\u306e\u8981\u7d20\u306e \u306e \u2208 \u306e \u3002 {displaystyle vin V.}  \u6700\u826f\u306e\u8fd1\u4f3c\u306e\u30bf\u30b9\u30af\u306f\u5e38\u306b\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e\u4eba\u306b\u3068\u3063\u3066 \u30d0\u30c4 \u2208 \u30d0\u30c4 {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \u6700\u826f\u306e\u8fd1\u4f3c\u306e\u8981\u7d20\u304c\u3042\u308a\u307e\u3059 \u306e \u2217 \u3001 {displaystyle v^{*}\u3001} \u3057\u304b\u3057\u3001\u5f7c\u306f\u5fc5\u305a\u3057\u3082\u552f\u4e00\u306e\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6700\u826f\u306e\u8fd1\u4f3c\u306e\u8981\u7d20\u306f\u3001\u5b87\u5b99\u3067\u63a1\u7528\u3055\u308c\u305f\u898f\u7bc4\u306b\u4f9d\u5b58\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u3002 {displaystyle X.}  \u30e6\u30cb\u30bf\u30ea\u30a2\u30b9\u30b9\u30da\u30fc\u30b9\u3067 \u3055\u305b\u3066 \u30d0\u30c4 {displaystyle x} \u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u3092\u5099\u3048\u305f\u30b9\u30da\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059 \u27e8 de \u3001 de \u27e9 {displaystyle langle cdot\u3001cdot rangle} \u305d\u3057\u3066\u3001\u6a19\u6e96\u3092\u5165\u308c\u3066\u304f\u3060\u3055\u3044 \u30d0\u30c4 {displaystyle x} \u3053\u306e\u88fd\u54c1\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u307e\u3059\uff1a \u2016 \u30d0\u30c4 \u2016 = \u27e8 \u30d0\u30c4 \u3001 \u30d0\u30c4 \u27e9 \u3002 {displaystyle | x | = {sqrt {langle x\u3001xrangle}}}}  \u305d\u306e\u5f8c\u3001\u4e0e\u3048\u3089\u308c\u305f \u30d0\u30c4 \u2208 \u30d0\u30c4 {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \u6700\u9069\u306a\u8fd1\u4f3c\u306e\u8981\u7d20 \u306e \u2217 {displaystyle v^{*}} \u552f\u4e00\u306e\u3082\u306e\u3067\u3042\u308a\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u2200 \u306e \u2208 \u306e   \u27e8 \u30d0\u30c4  –  \u306e \u2217\u3001 \u306e \u27e9 = 0\u3002 {displaystyle forall {vin v} langle x-v^{*}\u3001vrangle = 0\u3002} \u95a2\u6570\u306e\u8fd1\u4f3c\u306e\u554f\u984c [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8fd1\u4f3c\u306f\u3001\u305d\u306e\u5f15\u6570\u306e\u3044\u305a\u308c\u304b\u306e\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u95a2\u6570\u306e\u5206\u6790\u5f62\u5f0f\u304c\u306a\u3044\u72b6\u6cc1\u3067\u4f7f\u7528\u3055\u308c\u3001\u540c\u6642\u306b\u3053\u306e\u672a\u77e5\u306e\u95a2\u6570\u306e\u5024\u306f\u3001\u305d\u306e\u5f15\u6570\u306e\u7279\u5b9a\u306e\u30bb\u30c3\u30c8\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u305f\u3068\u3048\u3070\u3001\u30d5\u30a3\u30fc\u30eb\u30c9\u6e2c\u5b9a\u306b\u57fa\u3065\u3044\u3066\u7dcf\u89b3\u30de\u30c3\u30d7\u3092\u6e96\u5099\u3059\u308b\u969b\u306e\u6c17\u8c61\u5b66\u3067\u306f\u3002 \u95a2\u6570\u306e\u8fd1\u4f3c\u306f\u3001so -called\u306e\u7dda\u5f62\u7d44\u307f\u5408\u308f\u305b\u3067\u305d\u308c\u3092\u6301\u53c2\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u30d9\u30fc\u30b9\u95a2\u6570 [4] \u3002\u7279\u5b9a\u306e\u95a2\u6570\u3092\u5c0e\u5165\u3059\u308b\u8fd1\u4f3c\u95a2\u6570\u304b\u3089\u3001\u88dc\u9593\u306e\u5834\u5408\u306e\u3088\u3046\u306b\u3001\u7279\u5b9a\u306e\u30dd\u30a4\u30f3\u30c8\u3092\u901a\u904e\u3059\u308b\u3053\u3068\u306f\u5fc5\u9808\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6570\u5b66\u7684\u306a\u89b3\u70b9\u304b\u3089\u3001\u95a2\u6570\u306e\u8fd1\u4f3c f {displaystyle f} \u30d2\u30eb\u30d0\u30fc\u30c8\u306e\u7279\u5b9a\u306e\u30b9\u30da\u30fc\u30b9\u3067 h {displaystyle h} \u7279\u5b9a\u306e\u95a2\u6570\u3092\u691c\u7d22\u3059\u308b\u554f\u984c\u3067\u3059 g \u2208 g \u3001 {displaystyle gin g\u3001} \u3069\u3053 g {displaystyle g} \u305d\u308c\u306f\u30b5\u30d6\u30d7\u30ea\u30b8\u30e7\u30f3\u3067\u3059 h \uff08 g \u2282 h \uff09\uff09 {displaystyle h\u3001\uff08gsubset h\uff09} \u305d\u306e\u3088\u3046\u306a\u8ddd\u96e2\uff08\u306e\u610f\u5473\u3067 h {displaystyle h} \u6a19\u6e96\uff09\u9593 f {displaystyle f} a g {displaystyle g} \u5f7c\u5973\u306f\u3067\u304d\u308b\u3060\u3051\u4f4e\u304b\u3063\u305f\u3002 \u95a2\u6570\u306e\u8fd1\u4f3c\u306f\u3001\u8fd1\u4f3c\u8aa4\u5dee\u3068\u547c\u3070\u308c\u308b\u30a8\u30e9\u30fc\u3092\u5f15\u304d\u8d77\u3053\u3057\u307e\u3059 [5] \u3002\u88dc\u9593\u306b\u95a2\u9023\u3059\u308b\u8fd1\u4f3c\u306e\u5927\u304d\u306a\u5229\u70b9\u306f\u3001\u9069\u5207\u306b\u63d0\u793a\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u8fd1\u4f3c\u95a2\u6570\u304c\u9ad8\u3044\u4e8c\u5ea6\u591a\u9805\u5f0f\u3067\u3042\u308b\u5fc5\u8981\u304c\u306a\u3044\u3053\u3068\u3067\u3059\uff08\u307e\u3063\u305f\u304f\u591a\u9805\u5f0f\u3067\u3042\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\uff09\u3002\u3053\u306e\u5834\u5408\u306e\u8fd1\u4f3c\u306f\u3001\u7279\u5b9a\u306e\u30a8\u30e9\u30fc\u95a2\u6570\u3092\u6700\u5c0f\u5316\u3059\u308b\u3068\u7406\u89e3\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u304a\u305d\u3089\u304f\u3053\u306e\u30a8\u30e9\u30fc\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u5c3a\u5ea6\u306f\u5e73\u5747\u5e73\u65b9\u6839\u30a8\u30e9\u30fc\u3067\u3059\u304c\u3001\u5e73\u5747\u30a8\u30e9\u30fc\u306a\u3069\u306e\u4ed6\u306e\u30a8\u30e9\u30fc\u95a2\u6570\u3082\u53ef\u80fd\u3067\u3059\u3002 \u591a\u304f\u306e\u8fd1\u4f3c\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u3082\u4eba\u6c17\u306e\u3042\u308b\u3082\u306e\u306e1\u3064\u306f\u3001\u5869\u57fa\u95a2\u6570\u304c\u7dda\u5f62\u95a2\u6570\u3067\u3042\u308b\u5834\u5408\u3001\u4e2d\u578b\u306e\u8fd1\u4f3c\u3068\u5747\u4e00\u306a\u8fd1\u4f3c\u3001\u7dda\u5f62\u8fd1\u4f3c\u3067\u3059\u3002 \u8fd1\u4f3c\u95a2\u6570\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u5f0f\u3067\u63d0\u793a\u3067\u304d\u307e\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u305d\u308c\u306f\u30ad\u30e3\u30e9\u30af\u30bf\u30fc\u3067\u3059\uff1a 2\u6b21\u5143\u304a\u3088\u30733\u6b21\u5143\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u5834\u5408\u3001\u8fd1\u4f3c\u3082\u7b56\u5b9a\u3067\u304d\u307e\u3059\u3002 \u2191  B.P. Demidowicz\u3001I.A\u3002\u30de\u30ed\u30f3\u3001 \u6570\u5024\u7684\u65b9\u6cd5 \u3001 \u90e82\u3001PWN\u3001\u30ef\u30eb\u30b7\u30e3\u30ef1965\u3002  \u2191 a b c  J.\u30ec\u30b0\u30e9\u30b9\u3001 \u6570\u5024\u5206\u6790\u306e\u5b9f\u7528\u7684\u306a\u65b9\u6cd5 \u3001Wnt\u3001Warsaw 1974\u3002  \u2191  M.J. Ka\u0142kowski\u3001K\u3002Magnucki\u3001 \u6709\u9650\u8981\u7d20\u30e1\u30bd\u30c3\u30c9\u306e\u6982\u8981 \u3001\u7de8\u30dd\u30ba\u30ca\u30f3\u5de5\u79d1\u5927\u5b66\u3001\u30dd\u30ba\u30ca\u30f31982\u3002  \u2191   Fortuna\u3001Macukow\u3001\u304a\u3088\u3073Winsowski1993\u25ba \u3001s\u3002 74\u3002  \u2191   Fortuna\u3001Macukow\u3001\u304a\u3088\u3073Winsowski1993\u25ba \u3001s\u3002 73\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12448#breadcrumbitem","name":"\u8fd1\u4f3c – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]