{"id":5678,"date":"2024-12-29T11:44:43","date_gmt":"2024-12-29T11:44:43","guid":{"rendered":"https:\/\/crownstar.com\/crownstar\/?page_id=5678"},"modified":"2024-12-30T14:14:40","modified_gmt":"2024-12-30T14:14:40","slug":"math-test","status":"publish","type":"page","link":"https:\/\/crownstar.com\/crownstar\/math-test\/","title":{"rendered":"Math Test"},"content":{"rendered":"\n

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

At first, we sample \"f(x)\" in the \"N\" (\"N\" is odd) equidistant points around \"x^\":

  <\/span>   <\/span>\"\[ f_k = f(x_k),\: x_k = x^+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\]\"<\/p>
where \"h\" is some step.
Then we interpolate points \"{(x_k,f_k)}\" by polynomial
<\/a>

(1) <\/span>   <\/span>\"\begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation*}\"<\/p>
Its coefficients \"{a_j}\" are found as a solution of system of linear equations:
<\/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>
Here are references to existing equations: (1<\/a>), (2<\/a>).
Here is reference to non-existing equation (??).<\/p><\/div>\n\n\n\n

\"Rendered<\/p><\/p>\n\n\n\n

\"Rendered<\/p><\/p>\n\n\n\n



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

\"Rendered<\/p><\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

At first, we sample in the ( is odd) equidistant points around :     where is some step.Then we interpolate points by polynomial (1)   Its coefficients are found as a solution of system of linear equations: (2)   Here are references to existing equations: (1), (2).Here is reference to non-existing equation (??).<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_eb_attr":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"class_list":["post-5678","page","type-page","status-publish","hentry"],"blocksy_meta":[],"aioseo_notices":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/pages\/5678","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/comments?post=5678"}],"version-history":[{"count":47,"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/pages\/5678\/revisions"}],"predecessor-version":[{"id":5800,"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/pages\/5678\/revisions\/5800"}],"wp:attachment":[{"href":"https:\/\/crownstar.com\/crownstar\/wp-json\/wp\/v2\/media?parent=5678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}