Transfer Functions and Resolvent Norm Approximation of Large Matrices

A unifying framework for methods employed in the approximation of the resolvent norm of nonnor-mal matrices is presented. This formulation uses specific transfer functions, and it provides new information about the approximation properties of these methods and their application in computing the pseudospectrum of matrices. 1. Introduction. We now know that the analysis of matrix-dependent algorithms is considerably more complicated when nonnormal matrices are involved; see for example [5]. In particular, several studies indicate that the eigenvalues of the matrix in question often provide insufficient or even misleading information [20]. This has been the motivation behind recent research on more reliable indicators as well as on methods for their practical computation. Several studies concur that a better accordance between theory and practice can be achieved