Topical Issue Applied and Numerical Linear Algebra (2/2)

The face recognition problem is a topical issue in computer vision. In this paper we propose a customized version of the orthogonalization via deflation algorithm to tackle this problem. We test the new proposed algorithm on two datasets: the well-known ORL dataset and an own face dataset, CTOVF; also, we compare our results (in terms of rate recognition and average quiery time) with the outcome of a standard algorithm in this class (dimension reduction methods using numerical linear algebra tools).

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Numerical linear algebra and examples in control

10.23919/acc.1983.4788087 ◽

1983 ◽

Author(s):

Alan J. Laub

Keyword(s):

Linear Algebra ◽

Numerical Linear Algebra

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Research in Numerical Linear Algebra and Numerical Methods for Large-Scale Least Squares and Other Problems.

10.21236/ada131400 ◽

1983 ◽

Author(s):

Robert J. Plemmons

Keyword(s):

Numerical Methods ◽

Least Squares ◽

Linear Algebra ◽

Large Scale ◽

Numerical Linear Algebra

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Conference: Three Decades of Numerical Linear Algebra at Berkeley

10.21236/ada264964 ◽

1993 ◽

Author(s):

James Demmel

Keyword(s):

Linear Algebra ◽

Numerical Linear Algebra

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

BIT Numerical Mathematics ◽

10.1007/s10543-021-00872-1 ◽

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 ) .

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