SPECTRAL PORTRAIT FOR NON-HERMITIAN LARGE SPARSE MATRICES

The spectral portrait of a matrix is the picture of its epsilon-spectr a for epsilon is an element of [epsilon(1),epsilon(2)], where an epsil on-spectrum of A is the union of all the eigenvalues of all the matric es A + Delta with parallel to Delta parallel to(2) less than or equal to epsilon parallel to A parallel to(2). The spectral portrait is, for example, useful to study the stability of various problems, or, as we illustrate in this paper, to visualize the condition number of an eig envalue. Some methods to estimate the spectral portrait already exist, but only for small matrices. We propose here a new algorithm for non hermitian large sparse matrices.