BOUNDING EIGENVECTORS OF A SYMMETRIC MATRIX

Abstract

This chapter describes bounding eigenvectors of a symmetric matrix. It presents algorithms where the convergence is at least linear. It presents a priori bounds in a finite number of arithmetic operations. By using the interval Newton method, it is possible to produce a posteriori and a priori bounds for eigenvectors corresponding to simple eigenvalues. The chapter presents a theorem that states that the real number r produced in the Algorithm I (real case) is the multiplicity of λ1. The r vectors xi for i = 1 (1)r ,thus, created are linearly independent eigenvectors to λ1. The chapter presents a similar theorem that states that the real number r produced in the Algorithm II (real case) is the multiplicity of λ1. The r vectors yi for i = 1(1)r ,thus, created are linearly independent eigenvectors to λ1.