Positive entries of stable matrices.
Properties of a covariance matrix with an application to -optimal design.
Residual norm behavior for Hybrid LSQR regularization
Hybrid LSQR represents a powerful method for regularization of large-scale discrete inverse problems, where ill-conditioning of the model matrix and ill-posedness of the problem make the solutions seriously sensitive to the unknown noise in the data. Hybrid LSQR combines the iterative Golub-Kahan bidiagonalization with the Tikhonov regularization of the projected problem. While the behavior of the residual norm for the pure LSQR is well understood and can be used to construct a stopping criterion,...
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices.
Similarities of discrete and continuous Sturm-Liouville problems.
Spectral properties of sign symmetric matrices.
Symmetric nonnegative realization of spectra.
The Direct and Inverse Spectral Problems for some Banded Matrices
2000 Mathematics Subject Classification: 15A29.In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
The general totally positive matrix completion problem with few unspecified entries.
The nonnegative -matrix completion problem.
The -matrix completion problem.
The (weakly) sign symmetric -matrix completion problems.
Unitary completions of complex symmetric and skew symmetric matrices.