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11	Lineární algebraické modelování úloh s nepřesnými daty / Lineární algebraické modelování úloh s nepřesnými daty Vasilík, Kamil January 2011 (has links) In this thesis we consider problems Ax b arising from the discretization of ill-posed problems, where the right-hand side b is polluted by (unknown) noise. It was shown in [29] that under some natural assumptions, using the Golub-Kahan iterative bidiagonalization the noise level in the data can be estimated at a negligible cost. Such information can be further used in solving ill-posed problems. Here we suggest criteria for detecting the noise revealing iteration in the Golub-Kahan iterative bidiagonalization. We discuss the presence of noise of different colors. We study how the loss of orthogonality affects the noise revealing property of the bidiagonalization.
12	Iterative tensor factorization based on Krylov subspace-type methods with applications to image processing UGWU, UGOCHUKWU OBINNA 06 October 2021 (has links) No description available. Applied Mathematics Inverse problems Iterative tensor decomposition Krylov subspaces Image and video processing Truncated iterations Tensor Arnoldi process Tensor Golub-Kahan bidiagonalization Tensor Lanczos process tensor SVD Randomized tensor SVD t-product Invertible linear transform