Lanczos τ-method regularization algorithm and its algebraic-programming implementation

Abstract

An algebraic algorithm is developed for computing an algebraic polynomial y _n of order n ∈ N in computer algebra systems. This polynomial is the optimal approximation of the solution y = y(x), x ∈ [a,b], to a system of linear differential equations with polynomial coefficients and initial conditions at a regular singular zero point of this equation in a space $C_{\left[ {a,b} \right]}^k$.