\ub2e4\uc74c\uacfc \uac19\uc740 \ubb38\uc81c\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790.<\/p>\n
\uc138 \uc810\uc744 \uc9c0\ub098\ub294 \uadf8\ub798\ud504\ub97c \uac16\ub294 \uc774\ucc28\ud568\uc218<\/span><\/p>\n \\(a_1 ,\\) \\(a_2 ,\\) \\(a_3\\)\uc774 \uc11c\ub85c \ub2e4\ub978 \uc2e4\uc218\uc774\uace0, \\(b_1 ,\\) \\(b_2 ,\\) \\(b_3\\)\uc774 \uc2e4\uc218\uc77c \ub54c, \uadf8\ub798\ud504\uac00 \uc138 \uc810 \\((a_1 ,\\, b_1 ),\\) \\((a_2 ,\\, b_2 ),\\) \\((a_3 ,\\, b_3 )\\)\uc744 \ubaa8\ub450 \uc9c0\ub098\ub294 \uc774\ucc28\ud568\uc218\uc758 \uc2dd\uc744 \uc5b4\ub5bb\uac8c \uad6c\ud560 \uac83\uc778\uac00?<\/p>\n<\/div>\n \ub9cc\uc57d \uc774\ucc28\ud568\uc218\uc758 \uc2dd\uc744 \\(y = ax^2 + bx + c \\)\ub77c\uace0 \ub454\ub2e4\uba74, \uc704 \ubb38\uc81c\ub294 \ub2e4\uc74c \uc5f0\ub9bd\uc77c\ucc28\ubc29\uc815\uc2dd\uc5d0\uc11c \ubbf8\uc9c0\uc218 \\(a,\\) \\(b,\\) \\(c\\)\ub97c \ucc3e\ub294 \ubb38\uc81c\uac00 \ub41c\ub2e4. \uadf8\ub807\ub2e4\uba74 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc774\ucc28\ud568\uc218\ub294 \\(L(x)\\)\uac00 \uc720\uc77c\ud560\uae4c? \\(L ‘ (x)\\)\uac00 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc774\ucc28\ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uc9c0\uae08\uae4c\uc9c0 \uc0b4\ud3b4\ubcf8 \ub0b4\uc6a9\uc744 \uc77c\ubc18\ud654\ud574 \ubcf4\uc790.<\/p>\n \ub2e4\uc74c\uacfc \uac19\uc774 \uc11c\ub85c \ub2e4\ub978 \\(n+1\\)\uac1c\uc758 \uc2e4\uc218\ub97c \uc0dd\uac01\ud558\uc790. \uac01 \\(i=0 ,\\,\\, 1,\\,\\, 2,\\,\\, \\cdots ,\\,\\, n\\)\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 \\(f_i\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4. \n\uc815\ub9ac 1.<\/span> \uc774\uc81c \\(g ‘\\)\uc774 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc774\uace0, \uadf8\ub798\ud504\uac00 \uc810 \n\uc815\ub9ac 2.<\/span> \uc0c1\uc218\uc640 \uacc4\uc218\uac00 \ubaa8\ub450 \uc2e4\uc218\uc774\uace0 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\uc2dd\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubca1\ud130\uacf5\uac04\uc744 \\(P_n ( \\mathbb{R})\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ubb3c\ub860, \uc774 \uacf5\uac04\uc5d0\uc11c \ubca1\ud130 \ud569\uacfc \uc2a4\uce7c\ub77c \uacf1\uc740, \ub2e4\ud56d\uc2dd \uc6b0\uc120 \\(B\\)\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc784\uc744 \ubcf4\uc774\uc790. \\(\\alpha _0 ,\\) \\(\\alpha _1 ,\\) \\(\\cdots ,\\) \\(\\alpha _n \\)\uc774 \uc2e4\uc218\uc774\uace0 \ub2e4\uc74c\uc73c\ub85c \\(B\\)\uac00 \\(P_n ( \\mathbb{R})\\)\uc744 \uc0dd\uc131\ud568\uc744 \ubcf4\uc774\uc790. \\(g\\)\uac00 \\(P_n ( \\mathbb{R})\\)\uc758 \uc6d0\uc18c\ub77c\uace0 \ud558\uc790. \uc989 \\(g\\)\uac00 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uac01 \\(i\\)\uc5d0 \ub300\ud558\uc5ec \n\uc815\ub9ac 3.<\/span> \uc815\ub9ac 3\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uae30\uc800 \\(B\\)\ub97c \ub77c\uadf8\ub791\uc8fc \uae30\uc800<\/span>(Lagrange basis)\ub77c\uace0 \ubd80\ub978\ub2e4. \ub610\ud55c \uadf8\ub798\ud504\uac00 (1)\uacfc \uac19\uc740 \\(n+1\\)\uac1c\uc758 \uc810\uc744 \uc9c0\ub098\ub294 \\(n\\)\ucc28 \uc774\ud558\uc758 \ub2e4\ud56d\uc2dd\uc744 (2), (3)\uacfc \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc815\uc758\ud55c \ub2e4\ud56d\uc2dd \\(g(x)\\)\ub97c \ub77c\uadf8\ub791\uc8fc \ub2e4\ud56d\uc2dd<\/span>(Lagrange polynomial) \ub610\ub294 \ub77c\uadf8\ub791\uc8fc \ubcf4\uac04 \ub2e4\ud56d\uc2dd<\/span>(Lagrange interpolating polynomial)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" \ub2e4\uc74c\uacfc \uac19\uc740 \ubb38\uc81c\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790. \uc138 \uc810\uc744 \uc9c0\ub098\ub294 \uadf8\ub798\ud504\ub97c \uac16\ub294 \uc774\ucc28\ud568\uc218 \\(a_1 ,\\) \\(a_2 ,\\) \\(a_3\\)\uc774 \uc11c\ub85c \ub2e4\ub978 \uc2e4\uc218\uc774\uace0, \\(b_1 ,\\) \\(b_2 ,\\) \\(b_3\\)\uc774 \uc2e4\uc218\uc77c \ub54c, \uadf8\ub798\ud504\uac00 \uc138 \uc810 \\((a_1 ,\\, b_1 ),\\) \\((a_2 ,\\, b_2 ),\\) \\((a_3 ,\\, b_3 )\\)\uc744 \ubaa8\ub450 \uc9c0\ub098\ub294 \uc774\ucc28\ud568\uc218\uc758 \uc2dd\uc744 \uc5b4\ub5bb\uac8c \uad6c\ud560 \uac83\uc778\uac00? \ub9cc\uc57d \uc774\ucc28\ud568\uc218\uc758 \uc2dd\uc744 \\(y = ax^2 + bx + c \\)\ub77c\uace0 \ub454\ub2e4\uba74, \uc704 \ubb38\uc81c\ub294 \ub2e4\uc74c \uc5f0\ub9bd\uc77c\ucc28\ubc29\uc815\uc2dd\uc5d0\uc11c…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[57],"tags":[],"class_list":["post-8985","post","type-post","status-publish","format-standard","hentry","category-linear-algebra"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8985","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=8985"}],"version-history":[{"count":39,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8985\/revisions"}],"predecessor-version":[{"id":9024,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/8985\/revisions\/9024"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=8985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=8985"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=8985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\\[
\n\\begin{cases}
\na \\left( a_1 \\right)^2 + b \\left( a_1 \\right) + c = b_1 \\\\[6pt]
\na \\left( a_2 \\right)^2 + b \\left( a_2 \\right) + c = b_2 \\\\[6pt]
\na \\left( a_3 \\right)^2 + b \\left( a_3 \\right) + c = b_3
\n\\end{cases}\\]
\n\ub2e4\ub978 \ubc29\ubc95\uc73c\ub85c \ubb38\uc81c\uc758 \ud480\uc774\ubc95\uc5d0 \uc811\uadfc\ud574 \ubcf4\uc790.
\n\\[\\begin{aligned}
\n\\ell_1 (x) &= \\frac{x-a_2}{a_1 – a_2} \\frac{x-a_3}{a_1 – a_3} , \\\\[6pt]
\n\\ell_2 (x) &= \\frac{x-a_1}{a_2 – a_1} \\frac{x-a_3}{a_2 – a_3} , \\\\[6pt]
\n\\ell_3 (x) &= \\frac{x-a_1}{a_3 – a_1} \\frac{x-a_2}{a_3 – a_2} \\\\[6pt]
\n\\end{aligned}\\]
\n\uc774\ub77c\uace0 \ud558\uc790. \uc774\uc640 \uac19\uc774 \uc815\uc758\ub41c \ud568\uc218\uc5d0 \\(x=a_1 ,\\) \\(x=a_2 ,\\) \\(x=a_3\\)\uc744 \ub300\uc785\ud558\uba74 \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.
\n\\[\\begin{array}{ccc}
\n\\ell_1 (a_1 ) = 1 , & \\ell_1 (a_2 ) = 0 , & \\ell_1 (a_3 ) = 0, \\\\[6pt]
\n\\ell_2 (a_1 ) = 0 , & \\ell_2 (a_2 ) = 1 , & \\ell_2 (a_3 ) = 0, \\\\[6pt]
\n\\ell_3 (a_1 ) = 0 , & \\ell_3 (a_2 ) = 0 , & \\ell_3 (a_3 ) = 1 \\\\[6pt]
\n\\end{array}\\]
\n\uc774\uc81c
\n\\[ L(x) = b_1 \\,\\ell_1 (x) + b_2 \\,\\ell_2 (x) + b_3 \\,\\ell_3 (x) \\]
\n\ub77c\uace0 \uc815\uc758\ud558\uba74, \\(L(x)\\)\ub294 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc774\ucc28\ud568\uc218\uac00 \ub41c\ub2e4.<\/p>\n
\n\\[p(x) = L(x) – L ‘ (x)\\]
\n\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \ubc29\uc815\uc2dd \\(p(x) =0\\)\uc740 \uc11c\ub85c \ub2e4\ub978 \uc138 \uac1c\uc758 \uadfc \\(x = a_1 ,\\) \\(x = a_2 ,\\) \\(x = a_3 \\)\uc744 \uac00\uc9c4\ub2e4. \ub9cc\uc57d \\(p(x)\\)\uac00 \uc0c1\uc218\ud568\uc218\uac00 \uc544\ub2c8\ub77c\uba74, \\(p(x)\\)\ub294 \uc11c\ub85c \ub2e4\ub978 \uc138 \uac1c\uc758 \uc778\uc218 \\((x-a_1 ),\\) \\((x-a_2 ),\\) \\((x-a_3 )\\)\uc744 \uac00\uc9c4 \ub2e4\ud56d\uc2dd\uc774\ubbc0\ub85c 3\ucc28 \uc774\uc0c1\uc758 \ub2e4\ud56d\uc2dd\uc774 \ub41c\ub2e4. \uc774\uac83\uc740 \\(L(x)\\)\uc640 \\(L ‘ (x)\\)\uac00 \ubaa8\ub450 2\ucc28 \uc774\ud558\uc778 \ub2e4\ud56d\uc2dd\uc774\ub77c\ub294 \uc0ac\uc2e4\uc5d0 \ubaa8\uc21c\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(p(x)\\)\ub294 \uc0c1\uc218\uc774\uba70, \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)=0\\)\uc774\ub2e4. \uc989 \\(L(x)\\)\uc640 \\(L'(x)\\)\ub294 \ub3d9\uc77c\ud55c \uc774\ucc28\uc2dd\uc774\ub2e4.<\/p>\n\ub77c\uadf8\ub791\uc8fc\uc758 \ub2e4\ud56d\uc2dd<\/h4>\n
\n\\[ a_0 , \\,\\, a_1 ,\\,\\, a_2 , \\,\\, \\cdots \\,\\, a_n .\\]
\n\uadf8\ub9ac\uace0 \uc2e4\uc218 \\(n+1\\)\uac1c\ub97c \uc0dd\uac01\ud558\uc790.
\n\\[ b_0 , \\,\\, b_1 ,\\,\\, b_2 , \\,\\, \\cdots \\,\\, b_n .\\]
\n\uc774\uc81c \uc6b0\ub9ac\ub294 \uadf8\ub798\ud504\uac00 \\(n+1\\)\uac1c\uc758 \uc810
\n\\[(a_0 ,\\,\\, b_0 ) ,\\,\\, (a_1 ,\\,\\, b_1 ) ,\\,\\, \\cdots ,\\,\\, (a_n ,\\,\\, b_n ) \\tag{1}\\]
\n\uc744 \ubaa8\ub450 \uc9c0\ub098\uace0 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\ub97c \ucc3e\uace0\uc790 \ud55c\ub2e4.<\/p>\n
\n\\[f_i (x) = \\prod_{\\begin{gather}i \\ne j \\\\ 0 \\le j \\le n\\end{gather}} \\frac{x-a_j }{a_i -a_j } .\\tag{2}\\]
\n\ub9cc\uc57d \\(i \\ne j\\)\uc774\uba74 \\(f_i (x)\\)\ub97c \uc815\uc758\ud55c \ub2e4\ud56d\uc2dd\uc774 \uc778\uc218 \\((x-a_j )\\)\ub97c \uac00\uc9c0\ubbc0\ub85c
\n\\[f_i (a_j ) = 0\\]
\n\uc774\ub2e4. \ub9cc\uc57d \\(i = j\\)\uc774\uba74 \\(f_i ( a_i )\\)\ub294 \ubd84\ubaa8\uc640 \ubd84\uc790\uac00 \uac19\uc740 \ubd84\uc218\uc758 \uacf1\uc774\ubbc0\ub85c
\n\\[f_i (a_j ) = f_i (a_i ) = 1\\]
\n\uc774\ub2e4. \uc774\uc81c
\n\\[g(x) = b_0 \\,f_0 (x) + b_1 \\, f_1 (x) + \\cdots + b_n \\, f_n (x) \\tag{3}\\]
\n\ub77c\uace0 \ud558\uc790. \uac01 \\(f_i\\)\ub294 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\uc774\ubbc0\ub85c \\(g\\) \ub610\ud55c \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\uc774\ub2e4. \uadf8\ub9ac\uace0 \uac01 \\(j\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[\\begin{aligned}
\ng(a_j )
\n&= b_0 \\, f_0 (a_j ) + \\cdots + b_j \\, f_j ( a_j ) + \\cdots + b_n \\, f_n (a_j ) \\\\[6pt]
\n&= b_0 \\times 0 + \\cdots + b_j \\times 1 + \\cdots + b_n \\times 0
\n= b_j
\n\\end{aligned}\\]
\n\uc774\ubbc0\ub85c \ud568\uc218 \\(g\\)\uc758 \uadf8\ub798\ud504\ub294 \uc810 \\((a_j ,\\,\\, b_j )\\)\ub97c \uc9c0\ub09c\ub2e4.<\/p>\n
\n\\(a_0 , \\,\\, a_1 ,\\,\\, a_2 , \\,\\, \\cdots \\,\\, a_n\\)\uc774 \ubaa8\ub450 \ub2e4\ub978 \uc2e4\uc218\uc77c \ub54c, (2), (3)\uacfc \uac19\uc774 \uc815\uc758\ub41c \ud568\uc218 \\(g\\)\ub294 \uadf8\ub798\ud504\uac00 \\(n+1\\)\uac1c\uc758 \uc810
\n\\[(a_0 ,\\,\\, b_0 ) ,\\,\\, (a_1 ,\\,\\, b_1 ) ,\\,\\, \\cdots ,\\,\\, (a_n ,\\,\\, b_n )\\]
\n\uc744 \uc9c0\ub098\uace0 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\uc774\ub2e4.\n<\/p>\n<\/div>\n
\n\\[(a_0 ,\\,\\, b_0 ) ,\\,\\, (a_1 ,\\,\\, b_1 ) ,\\,\\, \\cdots ,\\,\\, (a_n ,\\,\\, b_n )\\]
\n\uc744 \ubaa8\ub450 \uc9c0\ub098\ub294 \ub2e4\ud56d\ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(p(x) = g(x) – g ‘ (x)\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \ubc29\uc815\uc2dd
\n\\[p(x) =0\\]
\n\uc740 \\(n+1\\)\uac1c\uc758 \uc11c\ub85c \ub2e4\ub978 \uadfc \\(x=a_0 ,\\) \\(x=a_1 ,\\) \\(\\cdots ,\\) \\(x=a_n \\)\uc744 \uac00\uc9c0\ub294 \ubc29\uc815\uc2dd\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c, \ub9cc\uc57d \\(p\\)\uac00 \uc0c1\uc218\ud568\uc218\uac00 \uc544\ub2c8\ub77c\uba74, \\(p\\)\ub294 \ucc28\uc218\uac00 \\(n+1\\) \uc774\uc0c1\uc778 \ub2e4\ud56d\ud568\uc218\uac00 \ub41c\ub2e4. \uadf8\ub7f0\ub370 \\(g\\)\uc640 \\(g ‘ \\)\uc774 \ubaa8\ub450 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\uc774\ubbc0\ub85c, \\(p\\)\ub294 \uc0c1\uc218\ud568\uc218\uc77c \uc218\ubc16\uc5d0 \uc5c6\ub2e4. \uc989 \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(p(x)=0\\)\uc774\ubbc0\ub85c, \\(g(x) = g’ (x)\\)\uc774\ub2e4. \uc989 \uadf8\ub798\ud504\uac00 (1)\uc5d0\uc11c \uc81c\uc2dc\ub41c \\(n+1\\)\uac1c\uc758 \uc810\uc744 \ubaa8\ub450 \uc9c0\ub098\uace0 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\uc2dd\uc740 (2), (3)\uacfc \uac19\uc774 \uc815\uc758\ub41c \ud568\uc218 \\(g\\)\uac00 \uc720\uc77c\ud558\ub2e4.<\/p>\n
\n\\(a_0 , \\,\\, a_1 ,\\,\\, a_2 , \\,\\, \\cdots \\,\\, a_n\\)\uc774 \ubaa8\ub450 \ub2e4\ub978 \uc2e4\uc218\uc77c \ub54c, \uadf8\ub798\ud504\uac00 \\(n+1\\)\uac1c\uc758 \uc810
\n\\[(a_0 ,\\,\\, b_0 ) ,\\,\\, (a_1 ,\\,\\, b_1 ) ,\\,\\, \\cdots ,\\,\\, (a_n ,\\,\\, b_n )\\]
\n\uc744 \uc9c0\ub098\uace0 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\ub294 \uc720\uc77c\ud558\uac8c \uacb0\uc815\ub41c\ub2e4.\n<\/p>\n<\/div>\n\ub2e4\ud56d\ud568\uc218 \uacf5\uac04<\/h4>\n
\n\\[ \\begin{aligned}
\np_1 (x) &= a_0 + a_1 \\, x^1 + a_2 \\,x^2 + \\cdots + a_n \\, x^n , \\\\[6pt]
\np_2 (x) &= b_0 + b_1 \\, x^1 + b_2 \\,x^2 + \\cdots + b_n \\, x^n
\n\\end{aligned}\\]
\n\uacfc \uc2e4\uc218 \\(c\\)\uc5d0 \ub300\ud558\uc5ec,
\n\\[\\begin{aligned}
\n(p_1 + p_2 )(x) &= (a_0 + b_0 ) + (a_1 + b_1 )x^1 + (a_2 +b_2 ) x^2 + \\cdots + (a_n + b_n ) x^n ,\\\\[6pt]
\n(cp_1 ) (x) &= (ca_0 ) + (ca_1 ) x^1 + (ca_2 ) x^2 + \\cdots + (ca_n )x^n
\n\\end{aligned}\\]
\n\uc73c\ub85c \uc815\uc758\ub418\uc5b4 \uc788\ub2e4. \uc774\uc81c (2)\uc640 \uac19\uc774 \uc815\uc758\ub41c \ub2e4\ud56d\ud568\uc218\uc758 \ubaa8\uc784
\n\\[B = \\left\\{ f_0 ,\\,\\, f_1 ,\\,\\, f_2 ,\\,\\, \\cdots ,\\,\\, f_n \\right\\}\\]
\n\uc774 \\(P_n ( \\mathbb{R})\\)\uc758 \uae30\uc800\uc784\uc744 \ubcf4\uc774\uc790.<\/p>\n
\n\\[\\alpha_0 \\, f_0 + \\alpha_1 \\, f_1 + \\cdots + \\alpha_n \\, f_n = 0 \\tag{4} \\]
\n\uc774\ub77c\uace0 \ud558\uc790. \uc774 \ub4f1\uc2dd\uc758 \uc88c\ubcc0\uc740 \ub2e4\ud56d\ud568\uc218\uc758 \uc77c\ucc28\uacb0\ud569\uc774\uace0, \uc6b0\ubcc0\uc740 \ud568\uc22b\uac12\uc774 \\(0\\)\uc778 \uc0c1\uc218\ud568\uc218\uc774\ub2e4. \uc989 \uc784\uc758\uc758 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.
\n\\[\\alpha_0 \\, f_0 (x) + \\alpha_1 \\, f_1 (x) + \\cdots + \\alpha_n \\, f_n (x) = 0 .\\]
\n\uc774 \uc2dd\uc5d0 \\(x=a_j \\)\ub97c \ub300\uc785\ud558\uba74
\n\\[\\alpha_0 \\, f_0 (a_j ) + \\alpha_1 \\, f_1 (a_j) + \\cdots + \\alpha_j \\, f_j (a_j ) + \\cdots + \\alpha_n \\, f_n (a_j) = 0 \\]
\n\uc774\ub2e4. \uadf8\ub7f0\ub370 \\(i\\ne j\\)\uc77c \ub54c \\(f_i (a_j ) =0\\)\uc774\uace0, \\(i=j\\)\uc77c \ub54c \\(f_i (a_i ) = 1\\)\uc774\ubbc0\ub85c, \uc704 \uc2dd\uc73c\ub85c\ubd80\ud130
\n\\[a_j = 0\\]
\n\uc744 \uc5bb\ub294\ub2e4. \uc5ec\uae30\uc11c \\(j\\)\ub294 \\(j=0,\\,\\,1,\\,\\,2,\\,\\, \\cdots ,\\,\\, n\\)\uc778 \uc815\uc218\uc774\ubbc0\ub85c, (4)\uc758 \uc88c\ubcc0\uc5d0 \uc788\ub294 \uc2a4\uce7c\ub77c\ub294 \ubaa8\ub450 \\(0\\)\uc774\ub2e4. \uc989 \\(B\\)\ub294 \uc77c\ucc28\ub3c5\ub9bd\uc774\ub2e4.<\/p>\n
\n\\[b_i = g(a_i ) ,\\,\\,\\, i=0,\\,\\,1,\\,\\,2,\\,\\,\\cdots ,\\,\\, n \\tag{5}\\]
\n\uc774\ub77c\uace0 \ud558\uace0
\n\\[\\phi (x) = b_0 \\, f_0 (x) + b_1 \\, f_1 (x) + \\cdots + b_n \\, f_n (x) \\]
\n\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \uc784\uc758\uc758 \\(j=0,\\,\\,1,\\,\\,2,\\,\\,\\cdots ,\\,\\, n\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.
\n\\[
\ng( a_j ) = b_j = b_0 \\, f_0 (a_j ) + b_1 \\, f_1 (a_j ) + \\cdots + b_j \\, f_j ( a_j ) + \\cdots + b_n \\, f_n ( a_j ) = \\phi (a_j ) .\\tag{6}\\]
\n\\(g\\)\uc640 \\(\\phi\\)\uac00 \ucc28\uc218\uac00 \\(n\\) \uc774\ud558\uc778 \ub2e4\ud56d\ud568\uc218\uc774\uace0, (5)\uc640 (6)\uc758\ud558\uc5ec \\(g\\)\uc640 \\(\\phi\\)\ub294 \\(n+1\\)\uac1c\uc758 \uc810
\n\\[(a_0 ,\\,\\, b_0 ) ,\\,\\, (a_1 ,\\,\\, b_1 ) ,\\,\\, \\cdots ,\\,\\, (a_n ,\\,\\, b_n ) \\]
\n\uc744 \ubaa8\ub450 \uc9c0\ub098\ub294 \uadf8\ub798\ud504\ub97c \uac00\uc9c4\ub2e4. \uc774\uc640 \uac19\uc740 \uc131\uc9c8\uc744 \uac00\uc9c0\ub294 \ud568\uc218\ub294 \uc720\uc77c\ud558\ubbc0\ub85c, \\(g = \\phi, \\) \uc989, \ubaa8\ub4e0 \\(x\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[g(x) = b_0 \\, f_0 (x) + b_1 \\, f_1 (x) + \\cdots + b_n \\, f_n (x)\\]
\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(g\\)\ub294 \\(B\\)\uc758 \uc6d0\uc18c\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4. \uc989 \\(B\\)\ub294 \\(P_n ( \\mathbb{R})\\)\uc744 \uc0dd\uc131\ud55c\ub2e4.\n<\/p>\n
\n\\(a_0 , \\,\\, a_1 ,\\,\\, a_2 , \\,\\, \\cdots \\,\\, a_n\\)\uc774 \ubaa8\ub450 \ub2e4\ub978 \uc2e4\uc218\uc77c \ub54c, (2)\uc640 \uac19\uc774 \uc815\uc758\ub41c \ud568\uc218 \\(f_i\\)\uc758 \ubaa8\uc784 \\(B\\)\ub294 \ubca1\ud130\uacf5\uac04 \\(P_n ( \\mathbb{R})\\)\uc758 \uae30\uc800\uc774\ub2e4.\n<\/p>\n<\/div>\n