Lanczos $\tau$-method optimal algorithm in APS for approximating the mathematical functions
<|reference_start|>Lanczos $\tau$-method optimal algorithm in APS for approximating the mathematical functions: 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.<|reference_end|>
@article{denisenko2006lanczos,
    title={Lanczos $\tau$-method optimal algorithm in APS for approximating the
  mathematical functions},
    author={P.N. Denisenko},
    journal={arXiv preprint arXiv:math/0603606},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0603606},
    primaryClass={math.NA cs.MS math.CA}
}