Convergence of algorithms of decomposition type for the eigenvalue problem
From MaRDI portal
Publication:749154
DOI10.1016/0024-3795(91)90004-GzbMath0712.65025MaRDI QIDQ749154
David S. Watkins, Ludwig Elsner
Publication date: 1991
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
eigenvaluecondition numbersshifting strategyGR algorithmnested subspace iterationquadratic asymptotic convergence ratetheory of convergence
Related Items
Lie algebra representations, nilpotent matrices, and the \(C\)-numerical range, Rational functions, Toda flows, and LR-like algorithms, A multishift QR iteration without computation of the shifts, Some remarks on the complex \(J\)-symmetric eigenproblem, Polynomial root computation by means of the LR algorithm, An algorithm for the single-input partial pole assignment problem, On the convergence of the \(QR\) algorithm with multishifts, Two connections between the \(SR\) and \(HR\) eigenvalue algorithms, The transmission of shifts and shift blurring in the QR algorithm, A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems, The LR Cholesky algorithm for symmetric hierarchical matrices, A-posteriori residual bounds for Arnoldi's methods for nonsymmetric eigenvalue problems, A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence, The parameterized đđ
algorithm for symplectic (butterfly) matrices, Nearly optimal scaling in the SR decomposition, A note on the double-shift \(QL\) algorithm, Rational \(QR\)-iteration without inversion, Computing a Hurwitz factorization of a polynomial, A QR-method for computing the singular values via semiseparable matrices, Skew-Symmetric Differential qd Algorithm, On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form, Matrix Bruhat decompositions with a remark on the QR(GR) algorithm, Convergence of the shifted \(QR\) algorithm on \(3\times{} 3\) normal matrices, Implicit QR algorithms for palindromic and even eigenvalue problems, \(SR\) and \(SZ\) algorithms for the symplectic (butterfly) eigenproblem, \(QR\)-like algorithms for eigenvalue problems, The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method, Diagonalization of complex symmetric matrices: generalized Householder reflections, iterative deflation and implicit shifts, On matrix differential equations and abstract FG algorithm, Convergence of the shifted $QR$ algorithm for unitary Hessenberg matrices, A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Das Verfahren der Treppeniteration und verwandte Verfahren zur Lösung algebraischer Eigenwertprobleme
- Rayleigh quotient iteration fails for nonsymmetric matrices
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- An analysis of the HR algorithm for computing the eigenvalues of a matrix
- Eigenvalues of Ax=lambdaBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form and the HR process
- Numerical linear algorithms and group theory
- On some algebraic problems in connection with general eigenvalue algorithms
- The condition numbers of the matrix eigenvalue problem
- Understanding the $QR$ Algorithm
- On Modern Matrix Iteration Processes of Bernoulli and Graeffe Type
- Chasing Algorithms for the Eigenvalue Problem
- ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION
- The ELR Method for Computing the Eigenvalues of a General Matrix
- A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
- Numerical Methods for Computing Angles Between Linear Subspaces
- Global Convergence of the Basic QR Algorithm On Hessenberg Matrices
- A Geometric Theory for the $QR$, $LU$ and Power Iterations
