{"id":25699594,"url":"https://github.com/kolosovpetro/anefficientmethodofsplineapproximation","last_synced_at":"2026-02-03T07:33:39.238Z","repository":{"id":278823852,"uuid":"919733397","full_name":"kolosovpetro/AnEfficientMethodOfSplineApproximation","owner":"kolosovpetro","description":"An efficient method of spline approximation for power 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unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["approximation","approximation-algorithms","math","mathematics","spline-approximation"],"created_at":"2025-02-25T03:15:52.689Z","updated_at":"2026-02-03T07:33:39.223Z","avatar_url":"https://github.com/kolosovpetro.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# An efficient method of spline approximation for power function\n\nLet $P(m, X, N)$ be an $m$-degree polynomial in $X\\in\\mathbb{R}$\nhaving fixed non-negative integers $m$ and $N$.\n\nEssentially, the polynomial $P(m, X, N)$ is a result of a rearrangement inside Faulhaber's formula\nin the context of Knuth's work entitled \"Johann Faulhaber and sums of powers\".\n\nIn this manuscript we discuss the approximation properties of polynomial $P(m,X,N)$.\n\nIn particular, the polynomial $P(m,X,N)$ approximates the odd power function $X^{2m+1}$ in a certain neighborhood\nof a fixed non-negative integer $N$ with a percentage error less than $1\\%$.\n\nBy increasing the value of $N$ the length of convergence interval with odd-power $X^{2m+1}$ also increases.\nFurthermore, this approximation technique is generalized for arbitrary non-negative exponent $j$ of the power function $X^j$\nby using splines.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkolosovpetro%2Fanefficientmethodofsplineapproximation","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fkolosovpetro%2Fanefficientmethodofsplineapproximation","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkolosovpetro%2Fanefficientmethodofsplineapproximation/lists"}