Numerical Linear Algebra

2011 ◽  
pp. 105-137 ◽  
Author(s):  
Lenka Čížková ◽  
Pavel Čížek
Keyword(s):  
Linear Algebra ◽  
Numerical Linear Algebra

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

Special Section on Iterative Methods in Numerical Linear Algebra

1994 ◽  
Vol 15 (3) ◽  
pp. 545-546
Author(s):  
Tom Manteuffel ◽  
Steve McCormick
Keyword(s):  
Iterative Methods ◽  
Linear Algebra ◽  
Special Section ◽  
Numerical Linear Algebra

A survey of power and energy efficient techniques for high performance numerical linear algebra operations

2014 ◽  
Vol 40 (10) ◽  
pp. 559-573 ◽  
Author(s):  
Li Tan ◽  
Shashank Kothapalli ◽  
Longxiang Chen ◽  
Omar Hussaini ◽  
Ryan Bissiri ◽  
...  
Keyword(s):  
Linear Algebra ◽  
Energy Efficient ◽  
High Performance ◽  
Numerical Linear Algebra ◽  
Power And Energy
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