Diffraction Problems and Inversion of Infinite Structured Matrices

Iterative inversion of structured matrices

Iterative processes for the inversion of structured matrices can be further improved by using a technique for compression and refinement via the least-squares computation. We review such processes and elaborate upon incorporation of this technique into the known frameworks.

TR-2002014: Iterative Inversion of Structured Matrices

Iterative processes for the inversion of structured matrices can be further improved by using a technique for compression and refinement via the least-squares computation. We review such processes and elaborate upon incorporation of this technique into the known frameworks.

Infinite Hankel Block Matrices, Extremal Problems

In the paper we consider a matrix version of the extremal Nehary problem [1],[4]. Our approach is based on the notion of a matrix analogue of the eigenvalue ρ2min. The notion of ρ 2 min was used in a number of the extremal interpolation problems [2],[3],[7]. We note that ρ2min is a solution of a nonlinear matrix inequality of the Riccati type [2],[6], [7]. Our approach coincides with the Adamja...

INFINITE MATRICES ASSOCIATED WITH DIFFRACTION BY AN APERTURE* Bt

Minimization problems for certain structured matrices

For given Z,B ∈ C, the problem of finding A ∈ C, in some prescribed class W , that minimizes ‖AZ − B‖ (Frobenius norm) has been considered by different authors for distinct classes W . Here, this minimization problem is studied for two other classes, which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. The pro...