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A Jacobi eigenreduction algorithm for definite matrix pairs

https://doi.org/10.1007/bf01388689
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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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Über explizite, halbimplizite und implizite Algorithmen zur endlichen und iterativen Transformation von Matrizenpaaren
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Perturbation Theory for Linear Operators
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Handbook for Automatic Computation
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Perturbation theory for linear operators
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Accurate Symmetric Eigenreduction by a Jacobi Method
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On quadratic convergence bounds for theJ-symmetric Jacobi method
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A note on a one-sided Jacobi algorithm
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Some convergent Jacobi-like procedures for diagonalising J-symmetric matrices
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On the global convergence of the Eberlein method for real matrices
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Fast Givens rotations for orthogonal similarity transformations
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Solution to the Eigenproblem by a norm reducing Jacobi type method
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Almost diagonal matrices with multiple or close eigenvalues
inferredcites →https://doi.org/10.1016/0024-3795(79)90094-6openalex-snapshot
Pertubation bounds for the definite generalized eigenvalue problem
inferredcites →https://doi.org/10.1016/0024-3795(91)90094-dopenalex-snapshot
On pairs of almost diagonal matrices
inferredcites →https://doi.org/10.1016/0024-3795(93)90258-popenalex-snapshot
Floating-point perturbations of Hermitian matrices
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The natural factor formulation of the stiffness for the matrix displacement method
inferredcites →https://doi.org/10.1016/0045-7825(83)90057-9openalex-snapshot
A global jacobi method for a symmetric indefinite problem Sx = λTx
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On Jacobi and Jacobi-Like Algorithms for a Parallel Computer
inferredcites →https://doi.org/10.1093/comjnl/15.3.271openalex-snapshot
The JK method: a procedure for finding the eigenvectors and eigenvalues of a real symmetric matrix
inferredcites →https://doi.org/10.1093/comjnl/18.1.74openalex-snapshot
A one-sided transformation method for the singular value decomposition and algebraic eigenproblem
inferredcites →https://doi.org/10.1093/comjnl/5.1.51openalex-snapshot
Adaptation of the Jacobi Method for a Computer with Magnetic-tape Backing Store
inferredcites →https://doi.org/10.1109/12.24289openalex-snapshot
A proof of convergence for two parallel Jacobi SVD algorithms
inferredcites →https://doi.org/10.1109/tc.1987.1676879openalex-snapshot
On the Schur Decomposition of a Matrix for Parallel Computation
inferredcites →https://doi.org/10.1117/12.942028openalex-snapshot
On The Equivalence And Convergence Of Parallel Jacobi SVD Algorithms
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Inversion of Matrices by Biorthogonalization and Related Results
inferredcites →https://doi.org/10.1137/0608064openalex-snapshot
On One-Sided Jacobi Methods for Parallel Computation
inferredcites →https://doi.org/10.1137/0610025openalex-snapshot
On the Convergence of the Cyclic Jacobi Method for Parallel Block Orderings
inferredcites →https://doi.org/10.1137/0612008openalex-snapshot
On the Quadratic Convergence of the Falk–Langemeyer Method
inferredcites →https://doi.org/10.1137/0613074openalex-snapshot
Jacobi’s Method is More Accurate than QR
inferredcites →https://doi.org/10.1137/0708060openalex-snapshot
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0710024openalex-snapshot
An Algorithm for Generalized Matrix Eigenvalue Problems
inferredcites →https://doi.org/10.1137/0727045openalex-snapshot
Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
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Solving Symmetric-Definite Quadratic $\lambda $-Matrix Problems without Factorization
inferredcites →https://doi.org/10.1137/0906007openalex-snapshot
The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays
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On Jacobi Methods for Singular Value Decompositions
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On Parallel Jacobi Orderings
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A Minimax Theory for Overdamped Networks
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Solutions Numeriques des Equations Algebriques
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Foundations of Linear Algebra.
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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
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A Continuous Approach for the Computation of the Hyperbolic Singular Value Decomposition
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On contractions in spaces with an indefinite metric: G-norms and spectral radii
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On quadratic convergence bounds for theJ-symmetric Jacobi method
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Implicit standard Jacobi gives high relative accuracy
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Constrained optimization of the overdetermined Zimmermann compressor for nonorthogonal joint matrix diagonalization
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Convergence to diagonal form of block Jacobi-type methods
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Accelerating the SVD Block-Jacobi Method
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Relative eigenvalue and singular value perturbations of scaled diagonally dominant matrices
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A GPU-based hyperbolic SVD algorithm
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Perturbation bounds for stable gyroscopic systems
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Detecting large definite Hermitian matrix pairs by $$\theta $$-subspace algorithms
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Accurate Eigenvalues of Some Generalized Sign Regular Matrices via Relatively Robust Representations
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Novel modifications of parallel Jacobi algorithms
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An indefinite variant of LOBPCG for definite matrix pencils
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Jacobi method for symmetric 4 × 4 matrices converges for every cyclic pivot strategy
inferred← citeshttps://doi.org/10.1007/s11075-017-0435-5openalex-snapshot
Globally convergent Jacobi methods for positive definite matrix pairs
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Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm
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A Kogbetliantz-type algorithm for the hyperbolic SVD
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Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices
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Trace minimization and definiteness of symmetric pencils
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Perturbations of the eigenprojections of a factorized Hermitian matrix
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Accurate singular value computation with the jacobi method
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Three-level parallel J-Jacobi algorithms for Hermitian matrices
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Relative perturbation theory for definite matrix pairs and hyperbolic eigenvalue problem
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Perturbation bounds for stable gyroscopic systems in motion about an unstable equilibrium position
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Quadratic convergence estimate of scaled iterates by J-symmetric Jacobi method
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Several observations on symplectic, Hamiltonian, and skew-Hamiltonian matrices
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A sort-Jacobi algorithm for semisimple lie algebras
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Block-oriented J-Jacobi methods for Hermitian matrices
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Full block J-Jacobi method for Hermitian matrices
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An indefinite LOBPCG type of algorithm for detecting a definite Hermitian matrix pair
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Approximate eigenvectors as preconditioner
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Relative perturbation theory for a class of diagonalizable Hermitian matrix pairs
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Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
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An implicit Jacobi-like method for computing generalized hyperbolic SVD
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Relative perturbation theory for hyperbolic singular value problem
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Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD
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Componentwise analysis of direct factorization of real symmetric and hermitian matrices
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A bound for the condition of a hyperbolic eigenvector matrix
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Accurate Factorization and Eigenvalue Algorithms for Symmetric DSTU and TSC Matrices
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