scholarly journals Rigorous Enclosures of Ellipsoids and Directed Cholesky Factorizations

2011 ◽  
Vol 32 (1) ◽  
pp. 262-285 ◽  
Author(s):  
Ferenc Domes ◽  
Arnold Neumaier
Keyword(s):  
Cholesky Factorizations

scholarly journals A Guide for Achieving High Performance with Very Small Matrices on GPU: A Case Study of Batched LU and Cholesky Factorizations

2018 ◽  
Vol 29 (5) ◽  
pp. 973-984 ◽  
Author(s):  
Azzam Haidar ◽  
Ahmad Abdelfattah ◽  
Mawussi Zounon ◽  
Stanimire Tomov ◽  
Jack Dongarra
Keyword(s):  
High Performance ◽  
Cholesky Factorizations

Incomplete Cholesky Factorizations with Limited Memory

1999 ◽  
Vol 21 (1) ◽  
pp. 24-45 ◽  
Author(s):  
Chih-Jen Lin ◽  
Jorge J. Moré
Keyword(s):  
Limited Memory ◽  
Cholesky Factorizations

scholarly journals Continuous analogues of matrix factorizations

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140585 ◽  
Author(s):  
Alex Townsend ◽  
Lloyd N. Trefethen
Keyword(s):  
Singular Value Decomposition ◽  
Infinite Series ◽  
Singular Value ◽  
Matrix Factorizations ◽  
One Dimension ◽  
Continuous Variables ◽  
Triangular Structure ◽  
Column Pivoting ◽  
Value Decomposition ◽  
Cholesky Factorizations

Analogues of singular value decomposition (SVD), QR, LU and Cholesky factorizations are presented for problems in which the usual discrete matrix is replaced by a ‘quasimatrix’, continuous in one dimension, or a ‘cmatrix’, continuous in both dimensions. Two challenges arise: the generalization of the notions of triangular structure and row and column pivoting to continuous variables (required in all cases except the SVD, and far from obvious), and the convergence of the infinite series that define the cmatrix factorizations. Our generalizations of triangularity and pivoting are based on a new notion of a ‘triangular quasimatrix’. Concerning convergence of the series, we prove theorems asserting convergence provided the functions involved are sufficiently smooth.

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