Representations of semigroups of idempotents
Let be the complex vector space of homogeneous linear polynomials in the variables . Suppose is a subgroup of , and is an irreducible character of . Let be the symmetry class of polynomials of degree with respect to and . For any linear operator acting on , there is a (unique) induced operator acting on symmetrized decomposable polynomials by In this paper, we show that the representation of the general linear group is equivalent to the direct sum of copies of a representation...
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,...
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.