國立虎尾科技大學 |

Kaczmarz Methods and Structured Matrix Decompositions.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Kaczmarz Methods and Structured Matrix Decompositions./
Author:	Yaniv, Yotam.
Description:	1 online resource (133 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
Contained By:	Dissertations Abstracts International85-11B.
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798382599786

Kaczmarz Methods and Structured Matrix Decompositions.
Yaniv, Yotam.

Kaczmarz Methods and Structured Matrix Decompositions. - 1 online resource (133 pages)

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2024.

Includes bibliographical references

In this dissertation, we discuss two distinct topics, both of which leverage randomized algorithms in numerical linear algebra. First we study three variants of the Kaczmarz method, a stochastic iterative method for solving linear systems. We propose a variant of the Kaczmarz method that uses additional memory to save on computation. We provide theoretical analysis and experimental results of the method, highlighting a gap in the literature. Additionally, we propose a variant of the Kaczmarz method in the data streaming setting that has an additional heavy ball momentum term. We prove a convergence bound for this method and analyze its merits experimentally given coherent data. Furthermore, we develop a variant of the Kaczmarz method for solving a latent class regression problem. Next we shift gears and discuss structured matrix factorizations. The first matrix factorization that we propose is a stratified non-negative matrix factorization. The aim of this method is to provide unsupervised dimensionality reduction on non-negative data that may be distributed across different locations. We prove a convergence bound for this method and analyze its performance on synthetic text, image and tabular data. Finally, we propose a hierarchically semi-separable matrix factorization method that uses random matrix sketching.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382599786Subjects--Topical Terms:

1069907
Applied mathematics.
Subjects--Index Terms:

Linear algebraIndex Terms--Genre/Form:

554714
Electronic books.

Kaczmarz Methods and Structured Matrix Decompositions.
LDR:02749ntm a22004097 4500 001 1146349
005 20240812064415.5
006 m o d
007 cr bn ---uuuuu
008 250605s2024 xx obm 000 0 eng d
020 $a 9798382599786
035 $a (MiAaPQ)AAI31297689
035 $a AAI31297689
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Yaniv, Yotam. $3 1471730
245 1 0 $a Kaczmarz Methods and Structured Matrix Decompositions.
264 0 $c 2024
300 $a 1 online resource (133 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: Dissertations Abstracts International, Volume: 85-11, Section: B.
500 $a Advisor: Bertozzi, Andrea;Hunter, Deanna M.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2024.
504 $a Includes bibliographical references
520 $a In this dissertation, we discuss two distinct topics, both of which leverage randomized algorithms in numerical linear algebra. First we study three variants of the Kaczmarz method, a stochastic iterative method for solving linear systems. We propose a variant of the Kaczmarz method that uses additional memory to save on computation. We provide theoretical analysis and experimental results of the method, highlighting a gap in the literature. Additionally, we propose a variant of the Kaczmarz method in the data streaming setting that has an additional heavy ball momentum term. We prove a convergence bound for this method and analyze its merits experimentally given coherent data. Furthermore, we develop a variant of the Kaczmarz method for solving a latent class regression problem. Next we shift gears and discuss structured matrix factorizations. The first matrix factorization that we propose is a stratified non-negative matrix factorization. The aim of this method is to provide unsupervised dimensionality reduction on non-negative data that may be distributed across different locations. We prove a convergence bound for this method and analyze its performance on synthetic text, image and tabular data. Finally, we propose a hierarchically semi-separable matrix factorization method that uses random matrix sketching.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Theoretical mathematics. $3 1180455
650 4 $a Mathematics. $3 527692
653 $a Linear algebra
653 $a Matrix factorizations
653 $a Theoretical analysis
653 $a Kaczmarz method
653 $a Machine learning
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
690 $a 0800
690 $a 0364
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 1180777
710 2 $a ProQuest Information and Learning Co. $3 1178819
773 0 $t Dissertations Abstracts International $g 85-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31297689 $z click for full text (PQDT)