Bounds for the singular values of Schwarz matrix

Some bounds for extreme singular values of a complex matrix

Dedicated to Professor H. M. Srivastava on the Occasion of his Seventieth Birth Anniversary

Some Bounds for the Singular Values of Matrices

Abstract We know that to estimate matrix singular values ( especially the largest and the smallest ones ) is an attractive topic in matrix theory and numerical analysis. In this note, we first provide a simple estimate for the smallest singular value σn(A) of n × n positive definite matrix A. Secondly, we obtain some simple estimates for the smallest singular value σn(A) and the largest singula...

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

Bounds for the Componentwise Distance to the Nearest Singular Matrix

The normwise distance of a matrix A to the nearest singular matrix is well known to be equal to ‖A‖/cond(A) for norms being subordinate to a vector norm. However, there is no hope to find a similar formula or even a simple algorithm for computing the componentwise distance to the nearest singular matrix for general matrices. This is because Rohn and Poljak [7] showed that this is an NP -hard pr...

Verified Bounds for Singular Values, in Particular for the Spectral Norm of a Matrix and Its Inverse

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of ...