New Numerical Algorithm for Deflation of Infinite and Zero Eigenvalues and Full Solution of Quadratic Eigenvalue Problems (CROSBI ID 287233)
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Podaci o odgovornosti
Drmač, Zlatko ; Šain Glibić, Ivana
engleski
New Numerical Algorithm for Deflation of Infinite and Zero Eigenvalues and Full Solution of Quadratic Eigenvalue Problems
This article presents a new method for computing all eigenvalues and eigenvectors of quadratic matrix pencil.It is an upgrade of the quadeig algorithm by Hammarlinget al., which attempts to reveal and remove by deflation a certain number of zero and infinite eigenvalues before QZ iterations. Proposed modifications of the quadeig framework are designed to enhance backward stability and to make the process of deflating infinite and zero eigenvalues more numerically robust. In particular, careful preprocessing allows scaling invariant/component-wise backward error and thus a better condition number. Further, using an upper triangular version of the Kronecker canonical form enables deflating additional infinite eigenvalues, in addition to those inferred from the rank of M. Theoretical analysis and empirical evidence from thorough testing of the software implementation confirm superior numerical performances of the proposed method.
eigenvalues ; quadratic eigenvalue problem ; QR factorization ; QZ method ; backward error ; infinite eigenvalues
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Podaci o izdanju
46 (4)
2020.
3401831
32
objavljeno
0098-3500
1557-7295
10.1145/3401831