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Linear and Multilinear Algebra Volume 48, 2000 - Issue 1
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Original Articles

Optimal multilevel matrix algebra operators

Fabio di Benedetto Dipartimento di Matematica, Genova, 16146, ItalyVia Dodecaneso 35
&
Stefano serra Capizzano Dipartimento di Informatica, pisa, 56100, ItalyCorso Italia 40
Pages 35-66 | Published online: 31 Mar 2008

Citations (16)

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Read on this site (3)

Ze-Jia Xie, Xiao-Qing Jin & Vai-Kuong Sin. (2020) An optimal preconditioner for tensor equations involving Einstein product. Linear and Multilinear Algebra 68:5, pages 886-902.
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Xiao-Qing Jin & Yi-Min Wei. (2007) A short note on singular values of optimal and superoptimal preconditioned matrices. International Journal of Computer Mathematics 84:8, pages 1261-1263.
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Fabio Di Benedetto & Stefano Serra Capizzano. (2002) A Note on the Superoptimal Matrix Algebra Operators. Linear and Multilinear Algebra 50:4, pages 343-372.
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Articles from other publishers (13)

Ivo Dravins, Stefano Serra-CapizzanoMaya Neytcheva. (2024) Spectral Analysis of Preconditioned Matrices Arising from Stage-Parallel Implicit Runge–Kutta Methods of Arbitrarily High Order. SIAM Journal on Matrix Analysis and Applications 45:2, pages 1007-1034.
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Andrea Adriani, Stefano Serra-Capizzano & Cristina Tablino-Possio. (2024) Clustering/Distribution Analysis and Preconditioned Krylov Solvers for the Approximated Helmholtz Equation and Fractional Laplacian in the Case of Complex-Valued, Unbounded Variable Coefficient Wave Number μ. Algorithms 17:3, pages 100.
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V. B. Kiran Kumar, M. N. N. Namboodiri & Rahul Rajan. (2019) A short survey on preconditioners and Korovkin-type theorems. The Journal of Analysis 29:2, pages 425-447.
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Stefano Cipolla, Carmine Di Fiore, Fabio Durastante & Paolo Zellini. (2018) Regularizing properties of a class of matrices including the optimal and the superoptimal preconditioners. Numerical Linear Algebra with Applications 26:2.
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ZhaoLin Jiang & TingTing Xu. (2015) Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra. Science China Mathematics 59:2, pages 351-366.
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Zhaolin Jiang, Tingting Xu & Fuliang Lu. (2014) Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra. Abstract and Applied Analysis 2014, pages 1-8.
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Xiao-Qing Jin & Fu-Rong Lin. (2009) Block preconditioners with circulant blocks for general linear systems. Computers & Mathematics with Applications 58:7, pages 1309-1319.
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Fabio Di Benedetto. (2009) Gram Matrices of Fast Algebras Have a Rank Structure. SIAM Journal on Matrix Analysis and Applications 31:2, pages 526-545.
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Claudio Estatico & Stefano Serra-Capizzano. (2008) Superoptimal approximation for unbounded symbols. Linear Algebra and its Applications 428:2-3, pages 564-585.
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Stefano Serra-Capizzano. (2007) The spectral approximation of multiplication operators via asymptotic (structured) linear algebra. Linear Algebra and its Applications 424:1, pages 154-176.
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Fabio Di Benedetto, Claudio Estatico & Stefano Serra Capizzano. (2005) Superoptimal Preconditioned Conjugate Gradient Iteration for Image Deblurring. SIAM Journal on Scientific Computing 26:3, pages 1012-1035.
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F. Costabile & S. Serra Capizzano. (2002) Komleva-type expansions and asymptotics for linear operators. Computers & Mathematics with Applications 43:6-7, pages 799-820.
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Stefano Serra Capizzano. (2002) Matrix algebra preconditioners for multilevel Toeplitz matrices are not superlinear. Linear Algebra and its Applications 343-344, pages 303-319.
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