Examinando por Materia "Espacio de Banach"

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    A numerical algorithm for calculating eigenvalues of preconditioned Toeplitz matrices
    (Universidad del Valle, 2025) Montenegro Parra, Julián Andrés; Bogoya Ramírez, Manuel
    This thesis addresses the problem of finding eigenvalues for preconditioned Toeplitz matrices based on a conjecture made by Professor Manuel Bogoya et al. In many cases, working with an ill-conditioned matrix can be computationally expensive. This is measured by what is known as the condition number of the matrix. The effect of preconditioning is to attempt to reduce this condition number so that the matrix is less sensitive to perturbations, that is, to small changes. Various types of numerical algorithms have been implemented to find the spectrum of Toeplitz matrices, and simple-loop theory allows for the derivation of asymptotic expansions for this type of matrix Tn(f) generated by a symbol f. However, this theory is not available in the context of preconditioned Toeplitz matrices.