Matrix pencils: Theory, applications, and numerical methods

DOI10.1007/BF01098963zbMath0783.15004OpenAlexW2025246398MaRDI QIDQ1191246

Khakim D. Ikramov

Publication date: 27 September 1992

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01098963

zbMATH Keywords

normal formsgeneralized eigenvalue problemresearch surveymatrix pencilseigenvalue sensitivityHermitian pencilssymmetric pencils

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02)

Related Items

On the minimal ranks of matrix pencils and the existence of a best approximate block-term tensor decomposition, Distinguishability of the descriptor systems with regular pencil, Gabor-type frames for signal processing on graphs, Calculating a function of a matrix with a real spectrum, Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors, A dual basis approach to multidimensional scaling, Fluctuating-rate model with multiple gene states, Analytic functional calculus for two operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Matrices and indefinite scalar products
• Finding a positive definite linear combination of two Hermitian matrices
• An algorithm for the symmetric generalized eigenvalue problem
• A note on locating eigenvalues
• Lanczos algorithms and field of value rotations for symmetric matrix pencils
• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• Residual error bounds of generalized eigenvalue systems
• HMDR and FMDR algorithms for the generalized eigenvalue problem
• Eigenvalues of Ax=lambdaBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form and the HR process
• The perturbation bounds for eigenspaces of a definite matrix-pair
• A global Jacobi method for a symmetric indefinite problem Sx=lambdaTx
• Simultaneous block diagonalization of two real symmetric matrices
• The number of vectors jointly annihilated by two real quadratic forms determines the inertia of matrices in the associated pencil
• On the maximal number of linearly independent real vectors annihilated simultaneously by two real quadratic forms
• Definite and semidefinite matrices in a real symmetric matrix pencil
• Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue
• Numerical range of a matrix: Some effective criteria
• Pencils of real symmetric matrices and the numerical range
• Perturbation bounds for the definite generalized eigenvalue problem
• A recurring theorem about pairs of quadratic forms and extensions: A survey
• A note on Stewart's theorem for definite matrix pairs
• Perturbation theorems for the generalized eigenvalue problem
• Solution of linear algebraic systems with rectangular matrices
• The role of symmetric matrices in the study of general matrices
• Note on the Factorization of a Square Matrix into Two Hermitian or Symmetric Matrices
• On the Field of Values of a Matrix
• The Factorization of a Square Matrix Into Two Symmetric Matrices
• Exclusion Theorems and the Perturbation Analysis of the Generalized Eigenvalue Problem
• An improved computational technique for perturbations of the generalized symmetric linear algebraic eigenvalue problem
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• Gershgorin Theory for the Generalized Eigenvalue Problem Ax = λBx
• On the Convergence of Cyclic Jacobi Methods
• A General Matrix Eigenvalue Algorithm
• A Stable Generalized Eigenvalue Problem
• Das Jacobi-Verfahren fürAx = λBx
• Algorithm 646
• The Rotation of Eigenvectors by a Perturbation. III
• Reduction of a band-symmetric generalized eigenvalue problem
• On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$
• An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem
• On Simultaneous Hermitian Congruence Transformations of Matrices
• An Extremum Property of Sums of Eigenvalues