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 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.

For details see math.NA/0603606