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A note on Oishi’s lower bound for the smallest singular value of linearized Galerkin equations
Citation Link: https://doi.org/10.15480/882.13373
Publikationstyp
Journal Article
Date Issued
2024-02-09
Sprache
English
TORE-DOI
Volume
41
Issue
2
Start Page
1097
End Page
1104
Citation
Japan Journal of Industrial and Applied Mathematics 41 (2): 1097-1104 (2024)
Publisher DOI
Scopus ID
Publisher
Springer
Recently Oishi published a paper allowing lower bounds for the minimum singular value of coefficient matrices of linearized Galerkin equations, which in turn arise in the computation of periodic solutions of nonlinear delay differential equations with some smooth nonlinearity. The coefficient matrix of linearized Galerkin equations may be large, so the computation of a valid lower bound of the smallest singular value may be costly. Oishi’s method is based on the inverse of a small upper left principal submatrix, and subsequent computations use a Schur complement with small computational cost. In this note some assumptions are removed and the bounds improved. Furthermore a technique is derived to reduce the total computationally cost significantly allowing to treat infinite dimensional matrices.
Subjects
65F45
Bound for the norm of the inverse of a matrix
Galerkin’s equation
Minimum singular value
Nonlinear delay differential equation
Schur complement
DDC Class
510: Mathematics
Publication version
publishedVersion
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s13160-024-00645-7.pdf
Type
Main Article
Size
1.11 MB
Format
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