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

P. N. Denisenko

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

Numerical Analysis 2007-05-23 v1 Mathematical Software Classical Analysis and ODEs

Authors: P. N. Denisenko

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.

Keywords

matrix algorithms

Cite

@article{arxiv.math/0603606,
  title  = {Lanczos $\tau$-method optimal algorithm in APS for approximating the mathematical functions},
  author = {P. N. Denisenko},
  journal= {arXiv preprint arXiv:math/0603606},
  year   = {2007}
}

Comments

10 pages. Based on a talk given at the Workshop on Symbolic Calculations and Exact Methods in Mathematical Physics, Kiev, June 20-26, 2005

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

Abstract

Keywords

Cite

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