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Lanczos $\tau$-method optimal algorithm in APS for approximating the mathematical functions

P. N. Denisenko
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Abstract

A new procedure is constructed by means of APS in APLAN language. The procedure solves the initial-value problem for linear differential equations of order $k$ with polynomial coefficients and regular singularity in the initialization point in the interval $[a, b]$ and computes the algebraic polynomial $y_n$ of given order $n$. A new algorithm of Lanczos $\tau$-method is built for this procedure, the solution existence $y_n$ of the initial-value problem proved on this algorithm and also is proved the optimality by precision of order $k$ derivative of the initial-value problem solution.

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P. N. Denisenko. 2006-03-26. Lanczos $\tau$-method optimal algorithm in APS for approximating the mathematical functions. https://arxiv.org/abs/math/0603606

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