SIMULTANEOUS DETERMINATION OF ALL THE ZEROS OF A LINEAR COMBINATION OF LEGENDRE POLYNOMIAL

Abstract

An algorithm based on modified improved Ehrlich method is developed which using real arithmetic could find all the zeros of Legendre-, Shifted Legendre- and Doubly Shifted Legendre polynomials, simultaneously, using a three term recurrence relation. The only information required is degree of the polynomial. The algorithm also finds simultaneously all the zeros of a linear combination of these polynomials, requiring information about the number of terms and the coefficients in the linear combination. The same algorithm works for finding simultaneously all the zeros of real polynomials requiring information about its degree and coefficients.