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On Jacobi Methods for Singular Value Decompositions

https://doi.org/10.1137/0908064
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Das Jacobi‐Verfahren für Ax = λ Bx
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Elektronische Datenverarbeitung
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The Jacobi Method for Real Symmetric Matrices
inferredcites →https://doi.org/10.1007/bf01386321openalex-snapshot
Note on the quadratic convergence of the cyclic Jacobi process
inferredcites →https://doi.org/10.1007/bf01396447openalex-snapshot
Computing theCS decomposition of a partitioned orthonormal matrix
inferredcites →https://doi.org/10.1007/bf01398880openalex-snapshot
On efficient implementations of Kogbetliantz's algorithm for computing the singular value decomposition
inferredcites →https://doi.org/10.1007/bf01407869openalex-snapshot
On the global convergence of the Eberlein method for real matrices
inferredcites →https://doi.org/10.1007/bf01462271openalex-snapshot
A convergent Jacobi method for solving the eigenproblem of arbitrary real matrices
inferredcites →https://doi.org/10.1007/bf01933422openalex-snapshot
On the quadratic convergence of a generalization of the Jacobi Method to arbitrary matrices
inferredcites →https://doi.org/10.1007/bf01939324openalex-snapshot
On the quadratic convergence of the Jabobi method for normal matrices
inferredcites →https://doi.org/10.1007/bf02163027openalex-snapshot
Singular value decomposition and least squares solutions
inferredcites →https://doi.org/10.1007/bf02165225openalex-snapshot
On the quadratic convergence of the special cyclic Jacobi method
inferredcites →https://doi.org/10.1007/bf02165467openalex-snapshot
Solution to the Eigenproblem by a norm reducing Jacobi type method
inferredcites →https://doi.org/10.1007/bfb0062104openalex-snapshot
A method for computing the generalized singular value decomposition
inferredcites →https://doi.org/10.1016/0024-3795(68)90023-2openalex-snapshot
An estimate for the norms of certain cyclic Jacobi operators
inferredcites →https://doi.org/10.1016/0024-3795(68)90042-6openalex-snapshot
Almost diagonal matrices with multiple or close eigenvalues
inferredcites →https://doi.org/10.1016/0024-3795(86)90171-0openalex-snapshot
Triangular processor array for computing singular values
inferredcites →https://doi.org/10.1016/0024-3795(86)90173-4openalex-snapshot
On the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition
inferredcites →https://doi.org/10.1016/0024-3795(86)90252-1openalex-snapshot
On the convergence of cyclic Jacobi-like processes
inferredcites →https://doi.org/10.1016/0024-3795(87)90031-0openalex-snapshot
On Kogbetliantz's SVD Algorithm in the Presence of Clusters
inferredcites →https://doi.org/10.1016/0024-3795(91)90094-dopenalex-snapshot
On pairs of almost diagonal matrices
inferredcites →https://doi.org/10.1016/0743-7315(85)90027-9openalex-snapshot
A parallel method for computing the generalized singular value decomposition
inferredcites →https://doi.org/10.1090/qam/88795openalex-snapshot
Solution of linear equations by diagonalization of coefficients matrix
inferredcites →https://doi.org/10.1090/s0002-9947-1960-0109825-2openalex-snapshot
The Cyclic Jacobi Method for Computing the Principal Values of a Complex Matrix
inferredcites →https://doi.org/10.1090/s0025-5718-1971-0297131-6openalex-snapshot
On Jacobi and Jacobi-Like Algorithms for a Parallel Computer
inferredcites →https://doi.org/10.1093/comjnl/15.3.274openalex-snapshot
On the quadratic convergence of the Jacobi method for normal matrices
inferredcites →https://doi.org/10.1115/1.3157781openalex-snapshot
The Symmetric Eigenvalue Problem
inferredcites →https://doi.org/10.1117/12.942028openalex-snapshot
On The Equivalence And Convergence Of Parallel Jacobi SVD Algorithms
inferredcites →https://doi.org/10.1137/0106005openalex-snapshot
Inversion of Matrices by Biorthogonalization and Related Results
inferredcites →https://doi.org/10.1137/0106008openalex-snapshot
On the Speed of Convergence of Cyclic and Quasicyclic Jacobi Methods for Computing Eigenvalues of Hermitian Matrices
inferredcites →https://doi.org/10.1137/0110029openalex-snapshot
Errata: A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors
inferredcites →https://doi.org/10.1137/0111032openalex-snapshot
On Cyclic Jacobi Methods
inferredcites →https://doi.org/10.1137/0702016openalex-snapshot
Calculating the Singular Values and Pseudo-Inverse of a Matrix
inferredcites →https://doi.org/10.1137/0906007openalex-snapshot
The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays
inferredcites →https://doi.org/10.1137/0907077openalex-snapshot
Computing the Generalized Singular Value Decomposition
inferredcites →https://doi.org/10.1137/1.9781611971163openalex-snapshot
The Symmetric Eigenvalue Problem
inferredcites →https://doi.org/10.56021/9781421407944openalex-snapshot
Matrix Computations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Advances in Jacobi Methods
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Matrix Eigenvalue Problems
inferred← citeshttps://doi.org/10.1007/978-3-642-21551-3_5openalex-snapshot
Numerical Linear Algebra
inferred← citeshttps://doi.org/10.1007/978-3-642-75536-1_48openalex-snapshot
On the Convergence of Cyclic Jacobi Methods
inferred← citeshttps://doi.org/10.1007/978-3-7091-6033-6_6openalex-snapshot
Quadratic Convergence of Scaled Iterates by Kogbetliantz Method
inferred← citeshttps://doi.org/10.1007/978-94-015-8196-7_52openalex-snapshot
Accurate Symmetric Eigenreduction by a Jacobi Method
inferred← citeshttps://doi.org/10.1007/bf01385728openalex-snapshot
On sharp quadratic convergence bounds for the serial Jacobi methods
inferred← citeshttps://doi.org/10.1007/bf01388689openalex-snapshot
A Jacobi eigenreduction algorithm for definite matrix pairs
inferred← citeshttps://doi.org/10.1007/bf01395779openalex-snapshot
Linear convergence of the row cyclic Jacobi and Kogbetliantz methods
inferred← citeshttps://doi.org/10.1007/bf01396349openalex-snapshot
A note on a one-sided Jacobi algorithm
inferred← citeshttps://doi.org/10.1007/s00211-014-0647-8openalex-snapshot
Convergence to diagonal form of block Jacobi-type methods
inferred← citeshttps://doi.org/10.1007/s10092-021-00415-8openalex-snapshot
On the global convergence of the block Jacobi method for the positive definite generalized eigenvalue problem
inferred← citeshttps://doi.org/10.1007/s10543-011-0333-5openalex-snapshot
A GPU-based hyperbolic SVD algorithm
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A contribution to the theory and practice of the block Kogbetliantz method for computing the SVD
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A Kogbetliantz-type algorithm for the hyperbolic SVD
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Arithmetical enhancements of the Kogbetliantz method for the SVD of order two
inferred← citeshttps://doi.org/10.1007/s11565-007-0027-8openalex-snapshot
Quadratic convergence of a special quasi-cyclic Jacobi method
inferred← citeshttps://doi.org/10.1016/0024-3795(90)90315-4openalex-snapshot
Relations between SVD and GSVD of Discrete regularization problems in standard and general form
inferred← citeshttps://doi.org/10.1016/j.amc.2008.12.086openalex-snapshot
Accuracy of two SVD algorithms for triangular matrices
inferred← citeshttps://doi.org/10.1016/j.amc.2010.09.020openalex-snapshot
Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices
inferred← citeshttps://doi.org/10.1016/j.laa.2014.02.024openalex-snapshot
On high relative accuracy of the Kogbetliantz method
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Parallel numerical linear algebra
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Recent Developments in Dense Numerical Linear Algebra
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Monitoring the stage of diagonalization in Jacobi-type methods
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Systolic Array Computation Of The SVD Of Complex Matrices
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New Fast and Accurate Jacobi SVD Algorithm. I
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New Fast and Accurate Jacobi SVD Algorithm. II
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Convergence of a Block‐Oriented Quasi‐Cyclic Jacobi Method
inferred← citeshttps://doi.org/10.1137/0610025openalex-snapshot
On the Convergence of the Cyclic Jacobi Method for Parallel Block Orderings
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A Singular Value Decomposition Updating Algorithm for Subspace Tracking
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Jacobi’s Method is More Accurate than QR
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On the Quadratic Convergence of the Serial Singular Value Decomposition Jacobi Methods for Triangular Matrices
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Computing the Generalized Singular Value Decomposition
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On the Parallel Implementation of Jacobi and Kogbetliantz Algorithms
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The Singular Value Decomposition: Anatomy of Optimizing an Algorithm for Extreme Scale
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The QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra Revisited
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