On the Convergence of Cyclic Jacobi-Like Processes
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TLDR
In this paper, a complex, column-and row-cyclic Jacobi-like process of the form A(k+1 ) = U ∗ k A( k )V k + F( k ), k⩾1, where U k, V k are unitary plane matrices, (F ( k )) is a sequence converging to diagonal form, and A ( 1 ) is an arbitrary n × n matrix.About:
This article is published in Linear Algebra and its Applications.The article was published on 1986-09-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Diagonal form & Matrix (mathematics).read more
Citations
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Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic
TL;DR: The modified Jacobi method recommended in this paper can be implemented as a reliable and highly accurate procedure for computing the SVD of general real matrices whenever the exact singular values do not exceed the underflow or overflow limits.
Journal ArticleDOI
On Jacobi methods for singular value decompositions
Vjeran Hari,Krevšimir Veselić +1 more
TL;DR: An improvement of the Jacobi singular value decomposition algorithm is proposed in this article, where the matrix is first reduced to a triangular form and the row-cyclic strategy preserves the triangularity.
Journal ArticleDOI
A Jacobi-like algorithm for computing the generalized Schur form of a regular pencil
J.P. Charlier,P. Van Dooren +1 more
TL;DR: A Jacobi-like scheme for computing the generalized Schur form of a regular pencil of matrices σB − A that can efficiently be implemented in parallel on a square array of processors and yields further insight in Stewart's algorithm.
Journal ArticleDOI
Convergence to diagonal form of block Jacobi-type methods
TL;DR: The paper provides sufficient conditions for the general sequential block Jacobi-type method to converge to the diagonal form for cyclic pivot strategies which are weakly equivalent to the column-cyclic strategy.
Journal ArticleDOI
On the quadratic convergence of the Falk-Langemeyer method
Ivan Slapni ccaron,Vjeran Hari +1 more
TL;DR: The Falk-Langemeyer method for solving real definite generalized eigenvalue problems is proved to be quadratically convergent under arbitrary cyclic pivot strategy if the eigenvalues of the problem are simple.
References
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The cyclic Jacobi method for computing the principal values of a complex matrix
George E. Forsythe,P. Henrici +1 more
TL;DR: In this paper, it was shown that the set of Xi is the limiting set of diagonal elements of a sequence of matrices which are generated from A recursively by plane rotations.
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Note on the quadratic convergence of the cyclic Jacobi process
Journal ArticleDOI
A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors of an Arbitrary Matrix
Journal ArticleDOI
Solution to the Eigenproblem by a norm reducing Jacobi type method
P. J. Eberlein,John Boothroyd +1 more
TL;DR: In this paper, a matrix T = T 1 T 2...T i... (or T -1) is constructed as a product of a sequence of two dimensional transformations T i, where T i is of the form RS where R is a rotation and S a complex rotation.
Contribution IIf 12 Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method
P. J. Eberlein,J. Boothroyd +1 more
TL;DR: In this paper, the rotational parameter x is determined by tan 2x= (a"",+a",,,)/(akk -a,,,,); that solution x being chosen such that after the transformation the norm of the k-th column is greater than or equal to the norm (m)th column.
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The cyclic Jacobi method for computing the principal values of a complex matrix
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