Residual bounds for some or all singular values

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...

Some bounds for extreme singular values of a complex matrix

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

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

Singular Values of Some Modular Functions *

. We denote by A1(N) and A0(N) the modular function fields with respect to Γ1(N) and Γ0(N) respectively. Let E be a set of triples of integers a = [a1, a2, a3] with the properties 0 < ai ≤ N/2 and ai 6= aj for i 6= j. For an element τ of complex upper half plane H, we denote by Lτ the lattice in C generated by 1 and τ . Let ℘(z;Lτ ) be the Weierstrass ℘-function relative to the lattice Lτ . For...

Bounds on Real Eigenvalues and Singular Values of Interval Matrices

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on one hand such interval matrices have many applications in mechanics and engineering, and on the other many results from classical matrix analysi...