{"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 class=\"wp-block-paragraph\"><\/p>\n\n\n\n\n\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-f4cad41\" data-block-id=\"f4cad41\"><p class=\"stk-block-text__text\">At first, we sample <img decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"\/> in the <img decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> (<img decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> is odd) equidistant points around <img decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-3d4037acb25d9f4838d94c006be4d29b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#94;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>: <p class=\"ql-center-displayed-equation\" style=\"line-height: 37px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-607407d64db813957976ba9e09d3b6c4_l3.png\" height=\"37\" width=\"377\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#32;&#102;&#95;&#107;&#32;&#61;&#32;&#102;&#40;&#120;&#95;&#107;&#41;&#44;&#92;&#58;&#32;&#120;&#95;&#107;&#32;&#61;&#32;&#120;&#94;&#43;&#107;&#104;&#44;&#92;&#58;&#32;&#107;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#78;&#45;&#49;&#125;&#123;&#50;&#125;&#44;&#92;&#100;&#111;&#116;&#115;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#78;&#45;&#49;&#125;&#123;&#50;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><br>where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"\/> is some step.<br>Then we interpolate points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-54ebc25fab8a3f087833bf91e9816a92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#40;&#120;&#95;&#107;&#44;&#102;&#95;&#107;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -5px;\"\/> by polynomial<br><a name=\"id4251117877\"><\/a><p class=\"ql-center-displayed-equation\" style=\"line-height: 55px;\"><span class=\"ql-right-eqno\"> (1) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-90b9e7e2804f1d17d7146fd4ba44de9a_l3.png\" height=\"55\" width=\"155\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#32;&#80;&#95;&#123;&#78;&#45;&#49;&#125;&#40;&#120;&#41;&#61;&#92;&#115;&#117;&#109;&#95;&#123;&#106;&#61;&#48;&#125;&#94;&#123;&#78;&#45;&#49;&#125;&#123;&#97;&#95;&#106;&#120;&#94;&#106;&#125;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><br>Its coefficients <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-e6e7601eff44e8a5f7892b23fbbbf29e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#95;&#106;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"15\" style=\"vertical-align: -6px;\"\/> are found as a solution of system of linear equations:<br><a name=\"id4065533911\"><\/a><p class=\"ql-center-displayed-equation\" style=\"line-height: 37px;\"><span class=\"ql-right-eqno\"> (2) <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-6998772f8434326cc9c05c954cd5f82e_l3.png\" height=\"37\" width=\"332\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#32;&#92;&#108;&#101;&#102;&#116;&#123;&#32;&#80;&#95;&#123;&#78;&#45;&#49;&#125;&#40;&#120;&#95;&#107;&#41;&#32;&#61;&#32;&#102;&#95;&#107;&#92;&#114;&#105;&#103;&#104;&#116;&#125;&#44;&#92;&#113;&#117;&#97;&#100;&#32;&#107;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#78;&#45;&#49;&#125;&#123;&#50;&#125;&#44;&#92;&#100;&#111;&#116;&#115;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#78;&#45;&#49;&#125;&#123;&#50;&#125;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><br>Here are references to existing equations: (<a href=\"#id4251117877\">1<\/a>), (<a href=\"#id4065533911\">2<\/a>).<br>Here is reference to non-existing equation (??).<\/p><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-b5c7e3adad8b299c268dc4f8c253f98a_l3.png\" height=\"282\" width=\"344\" class=\"ql-img-picture quicklatex-auto-format\" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-4a1c14b0047a4ae6c5e9156bc3a14c53_l3.png\" height=\"16\" width=\"185\" class=\"ql-img-picture quicklatex-auto-format\" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br><br><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><p class=\"ql-center-picture\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/crownstar.com\/crownstar\/wp-content\/ql-cache\/quicklatex.com-9a6639a08c0eee721e7dd0d6c9960ba1_l3.png\" height=\"204\" width=\"185\" class=\"ql-img-picture quicklatex-auto-format\" alt=\"Rendered by QuickLaTeX.com\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>At first, we sample in the ( is odd) equidistant points around : &nbsp; &nbsp; where is some step.Then we interpolate points by polynomial (1) &nbsp; Its coefficients are found as a solution of system of linear equations: (2) &nbsp; 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":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are references\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/crownstar.com\/crownstar\/math-test\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.10\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_GB\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Crownstar - A series of 40+ articles detailing the rise of  a 75 billion dollar industry\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Math Test - Crownstar\" \/>\n\t\t<meta property=\"og:description\" content=\"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are references\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/crownstar.com\/crownstar\/math-test\/\" \/>\n\t\t<meta property=\"og:image\" content=\"https:\/\/crownstar.com\/crownstar\/wp-content\/uploads\/sites\/15\/2024\/05\/Crownstar_Logo.png\" \/>\n\t\t<meta property=\"og:image:secure_url\" content=\"https:\/\/crownstar.com\/crownstar\/wp-content\/uploads\/sites\/15\/2024\/05\/Crownstar_Logo.png\" \/>\n\t\t<meta property=\"og:image:width\" content=\"676\" \/>\n\t\t<meta property=\"og:image:height\" content=\"407\" 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environments.\",\"url\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/\",\"telephone\":\"+31704449523\",\"logo\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/wp-content\\\/uploads\\\/sites\\\/15\\\/2024\\\/05\\\/Crownstar_Logo-1.png\",\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/math-test\\\/#organizationLogo\",\"width\":676,\"height\":407},\"image\":{\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/math-test\\\/#organizationLogo\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/math-test\\\/#webpage\",\"url\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/math-test\\\/\",\"name\":\"Math Test - Crownstar\",\"description\":\"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\\\[ f_k = f(x_k),\\\\: x_k = x^+kh,\\\\: k=-\\\\frac{N-1}{2},\\\\dots,\\\\frac{N-1}{2}\\\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\\\begin{equation} \\\\label{eq:poly}P_{N-1}(x)=\\\\sum_{j=0}^{N-1}{a_jx^j}\\\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\\\begin{equation} \\\\label{eq:sys}\\\\left{ P_{N-1}(x_k) = f_k\\\\right},\\\\quad k=-\\\\frac{N-1}{2},\\\\dots,\\\\frac{N-1}{2}\\\\end{equation}Here are references\",\"inLanguage\":\"en-GB\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/math-test\\\/#breadcrumblist\"},\"datePublished\":\"2024-12-29T11:44:43+00:00\",\"dateModified\":\"2024-12-30T14:14:40+00:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/#website\",\"url\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/\",\"name\":\"Crownstar\",\"description\":\"A series of 40+ articles detailing the rise of  a 75 billion dollar industry\",\"inLanguage\":\"en-GB\",\"publisher\":{\"@id\":\"https:\\\/\\\/crownstar.com\\\/crownstar\\\/#organization\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"Math Test - Crownstar","description":"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are references","canonical_url":"https:\/\/crownstar.com\/crownstar\/math-test\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BreadcrumbList","@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/crownstar.com\/crownstar#listItem","position":1,"name":"Home","item":"https:\/\/crownstar.com\/crownstar","nextItem":{"@type":"ListItem","@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#listItem","name":"Math Test"}},{"@type":"ListItem","@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#listItem","position":2,"name":"Math Test","previousItem":{"@type":"ListItem","@id":"https:\/\/crownstar.com\/crownstar#listItem","name":"Home"}}]},{"@type":"Organization","@id":"https:\/\/crownstar.com\/crownstar\/#organization","name":"Crownstar","description":"A series of 40+ articles detailing the rise of  a 75 billion dollar industry Crownstar is an technical service company that specializes in creating, integrating and deploying complex web applications for blockchain &amp; general environments.","url":"https:\/\/crownstar.com\/crownstar\/","telephone":"+31704449523","logo":{"@type":"ImageObject","url":"https:\/\/crownstar.com\/crownstar\/wp-content\/uploads\/sites\/15\/2024\/05\/Crownstar_Logo-1.png","@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#organizationLogo","width":676,"height":407},"image":{"@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#organizationLogo"}},{"@type":"WebPage","@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#webpage","url":"https:\/\/crownstar.com\/crownstar\/math-test\/","name":"Math Test - Crownstar","description":"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are references","inLanguage":"en-GB","isPartOf":{"@id":"https:\/\/crownstar.com\/crownstar\/#website"},"breadcrumb":{"@id":"https:\/\/crownstar.com\/crownstar\/math-test\/#breadcrumblist"},"datePublished":"2024-12-29T11:44:43+00:00","dateModified":"2024-12-30T14:14:40+00:00"},{"@type":"WebSite","@id":"https:\/\/crownstar.com\/crownstar\/#website","url":"https:\/\/crownstar.com\/crownstar\/","name":"Crownstar","description":"A series of 40+ articles detailing the rise of  a 75 billion dollar industry","inLanguage":"en-GB","publisher":{"@id":"https:\/\/crownstar.com\/crownstar\/#organization"}}]},"og:locale":"en_GB","og:site_name":"Crownstar - A series of 40+ articles detailing the rise of  a 75 billion dollar industry","og:type":"article","og:title":"Math Test - Crownstar","og:description":"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are references","og:url":"https:\/\/crownstar.com\/crownstar\/math-test\/","og:image":"https:\/\/crownstar.com\/crownstar\/wp-content\/uploads\/sites\/15\/2024\/05\/Crownstar_Logo.png","og:image:secure_url":"https:\/\/crownstar.com\/crownstar\/wp-content\/uploads\/sites\/15\/2024\/05\/Crownstar_Logo.png","og:image:width":676,"og:image:height":407,"article:published_time":"2024-12-29T11:44:43+00:00","article:modified_time":"2024-12-30T14:14:40+00:00","twitter:card":"summary_large_image","twitter:title":"Math Test - Crownstar","twitter:description":"[latexpage] [latexpage] At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^$: \\[ f_k = f(x_k),\\: x_k = x^+kh,\\: k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\]where $h$ is some step.Then we interpolate points ${(x_k,f_k)}$ by polynomial\\begin{equation} \\label{eq:poly}P_{N-1}(x)=\\sum_{j=0}^{N-1}{a_jx^j}\\end{equation}Its coefficients ${a_j}$ are found as a solution of system of linear equations:\\begin{equation} \\label{eq:sys}\\left{ P_{N-1}(x_k) = f_k\\right},\\quad k=-\\frac{N-1}{2},\\dots,\\frac{N-1}{2}\\end{equation}Here are 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