In the present paper, we give upper and lower bounds for the spectral norm of g-circulant matrix, whose the rst row entries are the classical Horadam numbers U (a,b) i . In addition, we also establish an explicit formula of the spectral norm for g-circulant matrix with the rst row ([U (a,b) 0 ] , [U (a,b) 1 ] , · · · , [U (a,b) n−1 ]).

We consider the problem of selecting the “best” subset of exactly k columns from an m× n matrix A. In particular, we present and analyze a novel two-stage algorithm that runs in O(min{mn2,m2n}) time and returns as output an m × k matrix C consisting of exactly k columns of A. In the first stage (the randomized stage), the algorithm randomly selects O(k log k) columns according to a judiciously-...

Nomenclature Hadamard product k k2, k kF spectral norm, Frobenius norm 0l m; 0l l m zero matrix, 0l l Il; 1l m l l identity matrix, l m ones matrix

We study complex-valued symmetric matrices. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. Consequently, we provide a sharp criterion for identifying those symmetric matrices whose spectral norm does not exceed one: such strongly stable matrices are usually sought in connection with convergent difference approximations ...

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 ...

The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...

We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text]...