Basic Research in the Mathematical Foundations of Stability Theory, Control Theory and Numerical Linear Algebra.

1979 ◽  
Author(s):  
Marvin Marcus ◽  
Morris Newman ◽  
Robert C. Thompson ◽  
Roy B. Leipnik ◽  
Henryk Minc
Keyword(s):  
Control Theory ◽  
Linear Algebra ◽  
Stability Theory ◽  
Basic Research ◽  
Numerical Linear Algebra ◽  
Mathematical Foundations

Algebraic Foundations of Stability Theory: A Computerized Linear Algebra Bibliography

1976 ◽  
Author(s):  
Marvin Marcus ◽  
Henryk Minc ◽  
Robert C. Thompson
Keyword(s):  
Linear Algebra ◽  
Stability Theory

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals Numerical Linear Algebra in Signal Processing Applications

2007 ◽  
Vol 2007 (1) ◽  
Author(s):  
Nicola Mastronardi ◽  
Gene H Golub ◽  
Shivkumar Chandrasekaran ◽  
Marc Moonen ◽  
Paul Van Dooren ◽  
...  
Keyword(s):  
Signal Processing ◽  
Linear Algebra ◽  
Numerical Linear Algebra
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