Numerical Methods for Eigenproblems
Christopher J. Zarowski · 2004
This chapter reviews the basic theory of eigenproblems beginning with the definition of eigenvalues, and eigenvectors. Diagonalizable matrices are emphasized but the Jordan decomposition theorem is reviewed. Similarity transformations are summarized. The problem of computing the matrix exponential is considered. Power methods and QR iterations for finding eigenvalues and eigenvectors are reviewed, including convergence analysis for the power methods.