New PCG based algorithms for the solution of Hermitian Toeplitz systems
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Publication:1373474
DOI10.1007/BF02575833zbMath0882.65019OpenAlexW2326028551MaRDI QIDQ1373474
Publication date: 5 March 1998
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02575833
generating functionpreconditioned conjugate gradient methodToeplitz linear systemslow-rank correction
Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)
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Cites Work
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- Spectral and computational properties of band symmetric Toeplitz matrices
- On the rate of convergence of the preconditioned conjugate gradient method
- Matrix structures in parallel matrix computations
- A practical algorithm to design fast and optimal band-Toeplitz preconditioners for Hermitian Toeplitz systems
- Multigrid methods for Toeplitz matrices
- Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems
- Spectra of multilevel Toeplitz matrices: Advanced theory via simple matrix relationships
- On the extreme eigenvalues of Hermitian (block) Toeplitz matrices
- On the extreme spectral properties of Toeplitz matrices generated by \(L^ 1\) functions with several minima/maxima
- C. G. preconditioning for Toeplitz matrices
- Optimal, quasi-optimal and superlinear band-Toeplitz preconditioners for asymptotically ill-conditioned positive definite Toeplitz systems
- On The Eigenvalues of Certain Hermitian Operators
- Stability of Methods for Solving Toeplitz Systems of Equations
- Superfast Solution of Real Positive Definite Toeplitz Systems
- Toeplitz Equations by Conjugate Gradients with Circulant Preconditioner
- Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions
- Superlinear PCG methods for symmetric Toeplitz systems
- Fast Band-Toeplitz Preconditioners for Hermitian Toeplitz Systems
- Preconditioning Strategies for Hermitian Toeplitz Systems with Nondefinite Generating Functions
- Analysis of Preconditioning Techniques for Ill-Conditioned Toeplitz Matrices
- Multigrid Methods for Symmetric Positive Definite Block Toeplitz Matrices with Nonnegative Generating Functions
- On a Matrix Algebra Related to the Discrete Hartley Transform
- An Algorithm for the Inversion of Finite Toeplitz Matrices
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