scholarly journals Generic symmetric matrix pencils with bounded rank

2020 ◽  
Vol 10 (3) ◽  
pp. 905-926
Author(s):  
Fernando De Terán ◽  
Andrii Dmytryshyn ◽  
Froilán Dopico
Keyword(s):  
Symmetric Matrix ◽  
Matrix Pencils ◽  
Bounded Rank

scholarly journals Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade

2020 ◽  
Vol 41 (3) ◽  
pp. 1033-1058
Author(s):  
Fernando De Terán ◽  
Andrii Dmytryshyn ◽  
Froilán M. Dopico
Keyword(s):  
Symmetric Matrix ◽  
Matrix Polynomials ◽  
Bounded Rank

scholarly journals Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations

2013 ◽  
Vol 438 (8) ◽  
pp. 3375-3396 ◽  
Author(s):  
Andrii Dmytryshyn ◽  
Bo Kågström ◽  
Vladimir V. Sergeichuk
Keyword(s):  
Symmetric Matrix ◽  
Matrix Equations ◽  
Matrix Pencils ◽  
Skew Symmetric Matrix

scholarly journals Variational and numerical methods for symmetric matrix pencils

1991 ◽  
Vol 43 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Peter Lancaster ◽  
Qiang Ye
Keyword(s):  
Numerical Methods ◽  
Symmetric Matrix ◽  
Rayleigh Quotient ◽  
Krylov Subspaces ◽  
Lanczos Algorithm ◽  
Convergence Properties ◽  
Recent Advances ◽  
Matrix Pencils

A review is presented of some recent advances in variational and numerical methods for symmetric matrix pencils λA – B in which A is nonsingular, A and B are hermitian, but neither is definite. The topics covered include minimax and maximin characterisations of eigenvalues, perturbation by semidefinite matrices and interlacing properties of real eigenvalues, Rayleigh quotient algorithms and their convergence properties, Rayleigh-Ritz methods employing Krylov subspaces, and a generalised Lanczos algorithm.

scholarly journals Symmetric matrix pencils

1991 ◽  
Vol 38 (1-3) ◽  
pp. 373-385 ◽  
Author(s):  
Beresford N. Parlett
Keyword(s):  
Symmetric Matrix ◽  
Matrix Pencils
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