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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,...