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An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem./
Author:	Camacho, Frankie.
Description:	1 online resource (149 pages)
Notes:	Source: Masters Abstracts International, Volume: 57-02.
Contained By:	Masters Abstracts International57-02(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355370751

An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.
Camacho, Frankie.

An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem. - 1 online resource (149 pages)

Source: Masters Abstracts International, Volume: 57-02.

Thesis (M.A.)

Includes bibliographical references

The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly large-scale problems, matrices themselves are often not directly accessible, but their actions as linear operators can be probed through matrix-vector multiplications. To solve such problems, matrix-free algorithms are the only viable option. In addition, algorithms that do multiple matrix-vector multiplications simultaneously (instead of sequentially), or so-called block algorithms, generally have greater parallel scalability that can prove advantageous on highly parallel, modern computer architectures.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355370751Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Camacho, Frankie. $3 1180987
245 1 3 $a An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.
264 0 $c 2017
300 $a 1 online resource (149 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 57-02.
500 $a Adviser: Yin Zhang.
502 $a Thesis (M.A.) $c Rice University $d 2017.
504 $a Includes bibliographical references
520 $a The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly large-scale problems, matrices themselves are often not directly accessible, but their actions as linear operators can be probed through matrix-vector multiplications. To solve such problems, matrix-free algorithms are the only viable option. In addition, algorithms that do multiple matrix-vector multiplications simultaneously (instead of sequentially), or so-called block algorithms, generally have greater parallel scalability that can prove advantageous on highly parallel, modern computer architectures.
520 $a In this work, we propose and study a new inverse-free, block algorithmic framework for generalized eigenvalue problems that is based on an extension of a recent framework called eigpen -- an unconstrained optimization formulation utilizing the Courant Penalty function. We construct a method that borrows several key ideas, including projected gradient descent, back-tracking line search, and Rayleigh-Ritz (RR) projection. We establish a convergence theory for this framework.
520 $a We conduct numerical experiments to assess the performance of the proposed method in comparison to two well-known existing matrix-free algorithms, as well as to the popular solver ARPACK as a benchmark (even though it is not matrix-free). Our numerical results suggest that the new method is highly promising and worthy of further study and development.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Rice University. $b Computational and Applied Mathematics. $3 1180983
773 0 $t Masters Abstracts International $g 57-02(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10670676 $z click for full text (PQDT)