{"id":103,"date":"2025-04-17T04:30:32","date_gmt":"2025-04-17T04:30:32","guid":{"rendered":"http:\/\/saegil-lab.kr\/?p=103"},"modified":"2025-08-27T04:20:08","modified_gmt":"2025-08-27T04:20:08","slug":"latex-%ec%97%b0%ec%8a%b5-2","status":"publish","type":"post","link":"https:\/\/saegil-lab.kr\/?p=103","title":{"rendered":"LaTeX \uc5f0\uc2b5 2"},"content":{"rendered":"\n

<\/p>\n\n\n\n

\"\LaTeX\"\uc5f0\uc2b5\uc6a9 2<\/p>\n\n\n\n

At first, we sample \"f(x)\" in the \"N\" (\"N\" is odd) equidistant points around \"x^*\":<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[f_k = f(x_k), \:x_k = x^* + kh, \:k=-\frac{N-1}{2}, \dots, \frac{N-1}{2}\]\"<\/p><\/p>\n\n\n\n

where \"h\" is some step.<\/p>\n\n\n\n

Then we interpolate points \"\{(x_k, f_k)\}\" by polynomial<\/p>\n\n\n\n

<\/a>

(1) <\/span>   <\/span>\"\begin{equation*} P_{N-1}(x) = \sum_{j=0}^{N-1}{a_jx^j}\end{equation*}\"<\/p><\/p>\n\n\n\n

It’s cofficients \"\{a_j\}\" are found as a solution of system of linear equations:<\/p>\n\n\n\n

<\/a>

(2) <\/span>   <\/span>\"\begin{equation*} \left\{ P_{N-1} (x_k) = f_k \right\}, \quad k= -\frac{N-1}{2}, \dots , \frac{N-1}{2}\end{equation*}\"<\/p><\/p>\n\n\n\n

Here are references to existing equations: (1<\/a>), (2<\/a>).<\/p>\n\n\n\n

Here is reference to non-existing equation (??).<\/p>\n","protected":false},"excerpt":{"rendered":"

\uc5f0\uc2b5\uc6a9 2 At first, we sample in the ( is odd) equidistant points around :     where is some step. Then we interpolate points by polynomial (1)   It’s cofficients are found as a solution of system of linear … \uacc4\uc18d \uc77d\uae30 →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-103","post","type-post","status-publish","format-standard","hentry","category-1"],"_links":{"self":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=103"}],"version-history":[{"count":14,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/103\/revisions"}],"predecessor-version":[{"id":118,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/103\/revisions\/118"}],"wp:attachment":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=103"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=103"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}