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Fast solvers for Toeplitz systems with applications to image restorationWen, Youwei., 文有為. January 2006 (has links)
published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy
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Fast solvers for Toeplitz systems with applications to image restorationWen, Youwei. January 2006 (has links)
Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.
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Fast iterative methods for solving Toeplitz and Toeplitz-like systemsNg, Kwok-po., 吳國寶. January 1992 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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Fast iterative methods for solving Toeplitz and Toeplitz-like systems /Ng, Kwok-po. January 1992 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1993. / Photocopy typescript.
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Novel structures for very fast adaptive filtersMcWhorter, Francis LeRoy January 1990 (has links)
No description available.
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A Note on Generation, Estimation and Prediction of Stationary ProcessesHauser, Michael A., Hörmann, Wolfgang, Kunst, Robert M., Lenneis, Jörg January 1994 (has links) (PDF)
Some recently discussed stationary processes like fractionally integrated processes cannot be described by low order autoregressive or moving average (ARMA) models rendering the common algorithms for generation estimation and prediction partly very misleading. We offer an unified approach based on the Cholesky decomposition of the covariance matrix which makes these problems exactly solvable in an efficient way. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing
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Preconditioning techniques for all-at-once linear systems arising from advection diffusion equationsLin, Xuelei 07 August 2020 (has links)
In this thesis, we mainly study preconditioning techniques for all-at-once linear systems arising from discretization of three types of time-dependent advection-diffusion equation: linear diffusion equation, constant-coefficients advection-diffusion equation, time-fractional sub-diffusion equation. The proposed preconditioners are used with Krylov subspace solvers. The preconditioner developed for linear diffusion equation is based on -circulant ap- proximation of temporal discretization. Diagonalizability, clustering of spectrum and identity-plus-low-rank decomposition are derived for the preconditioned matrix. We also show that generalized minimal residual (GMRES) solver for the preconditioned system has a linear convergence rate independent of matrix-size. The preconditioner for constant-coefficients advection-diffusion equation is based on approximating the discretization of advection term with a matrix diagonalizable by sine transform. Eigenvalues of the preconditioned matrix are proven to be lower and upper bounded by positive constants independent of discretization parameters. Moreover, as the preconditioner is based on spatial approximation, it is also applicable to steady-state problem. We show that GMRES for the preconditioned steady-state problem has a linear convergence rate independent of matrix size. The preconditioner for time-fractional sub-diffusion equation is based on approximat- ing the discretization of diffusion term with a matrix diagonalizable by sine transform. We show that the condition number of the preconditioned matrix is bounded by a constant independent of discretization parameters so that the normalized conjugate gradient (NCG) solver for the preconditioned system has a linear convergence rate independent of discretization parameters and matrix size. Fast implementations based on fast Fourier transform (FFT), fast sine transform (FST) or multigrid approximation are proposed for the developed preconditioners. Numerical results are reported to show the performance of the developed preconditioners
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Preconditioning techniques for all-at-once linear systems arising from advection diffusion equationsLin, Xuelei 07 August 2020 (has links)
In this thesis, we mainly study preconditioning techniques for all-at-once linear systems arising from discretization of three types of time-dependent advection-diffusion equation: linear diffusion equation, constant-coefficients advection-diffusion equation, time-fractional sub-diffusion equation. The proposed preconditioners are used with Krylov subspace solvers. The preconditioner developed for linear diffusion equation is based on -circulant ap- proximation of temporal discretization. Diagonalizability, clustering of spectrum and identity-plus-low-rank decomposition are derived for the preconditioned matrix. We also show that generalized minimal residual (GMRES) solver for the preconditioned system has a linear convergence rate independent of matrix-size. The preconditioner for constant-coefficients advection-diffusion equation is based on approximating the discretization of advection term with a matrix diagonalizable by sine transform. Eigenvalues of the preconditioned matrix are proven to be lower and upper bounded by positive constants independent of discretization parameters. Moreover, as the preconditioner is based on spatial approximation, it is also applicable to steady-state problem. We show that GMRES for the preconditioned steady-state problem has a linear convergence rate independent of matrix size. The preconditioner for time-fractional sub-diffusion equation is based on approximat- ing the discretization of diffusion term with a matrix diagonalizable by sine transform. We show that the condition number of the preconditioned matrix is bounded by a constant independent of discretization parameters so that the normalized conjugate gradient (NCG) solver for the preconditioned system has a linear convergence rate independent of discretization parameters and matrix size. Fast implementations based on fast Fourier transform (FFT), fast sine transform (FST) or multigrid approximation are proposed for the developed preconditioners. Numerical results are reported to show the performance of the developed preconditioners
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Circulant preconditioners for Toeplitz matrices and their applicationsin solving partial differential equations金小慶, Jin, Xiao-qing. January 1992 (has links)
published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy
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Optimal and suboptimal filtering for Toeplitz systemsJanuary 1979 (has links)
by Joseph E. Wall, Jr., Alan S. Willsky, Nils R. Sandell, Jr. / Bibliography: leaf [27] / Department of Energy Contract ERDA-E-(49-18)-2087
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