Abstract: A bisection method is presented for solving the eigenvalue problem of symmetric band matrices.This method is especially suitable for the case where only a few eigenpairs are needed. Further more,a modified strategy is also presented.The main idea is that firstly using the bisection for some steps to obtain an approximate eigenvalue,then Rayleigh Quotient Iteration is applied to extract the eigenvalue to a predifined accuracy.

Key words: Symmetric band matrix, matrix eiganvalue problem, bisection method, Rayleigh Quotient Iteraiton