Kirovograd State Technical University,

8 University Ave.,

25006 Kirovograd

UKRAINE

E-mail: pnden_osvita@yahoo.com

**An optimal algorithm for Lanczos tau-method of approximation
of the mathematical functions in APS**

**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

For details see math.NA/0603606