Part II A systolic array for numerical linear algebra

1993 ◽  
Vol 63 (1) ◽  
pp. 97-115
Keyword(s):  
Linear Algebra ◽  
Systolic Array ◽  
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

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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