scholarly journals Spectral condition‐number estimation of large sparse matrices

2019 ◽  
Vol 26 (3) ◽  
pp. e2235 ◽  
Author(s):  
Haim Avron ◽  
Alex Druinsky ◽  
Sivan Toledo
Keyword(s):  
Condition Number ◽  
Sparse Matrices ◽  
Spectral Condition ◽  
Large Sparse Matrices

scholarly journals The spectral condition number plot for regularization parameter evaluation

2019 ◽  
Vol 35 (2) ◽  
pp. 629-646 ◽  
Author(s):  
Carel F. W. Peeters ◽  
Mark A. van de Wiel ◽  
Wessel N. van Wieringen
Keyword(s):  
Condition Number ◽  
Regularization Parameter ◽  
Spectral Condition ◽  
Parameter Evaluation

An Efficient Parallel Algorithm for Extreme Eigenvalues of Sparse Nonsymmetric Matrices

1992 ◽  
Vol 6 (1) ◽  
pp. 98-111 ◽  
Author(s):  
S. K. Kim ◽  
A. T. Chrortopoulos
Keyword(s):  
Shared Memory ◽  
Message Passing ◽  
Sparse Matrices ◽  
Data Locality ◽  
Main Memory ◽  
Global Memory ◽  
Global Communication ◽  
Step Method ◽  
Arnoldi Algorithm ◽  
Large Sparse Matrices

Main memory accesses for shared-memory systems or global communications (synchronizations) in message passing systems decrease the computation speed. In this paper, the standard Arnoldi algorithm for approximating a small number of eigenvalues, with largest (or smallest) real parts for nonsymmetric large sparse matrices, is restructured so that only one synchronization point is required; that is, one global communication in a message passing distributed-memory machine or one global memory sweep in a shared-memory machine per each iteration is required. We also introduce an s-step Arnoldi method for finding a few eigenvalues of nonsymmetric large sparse matrices. This method generates reduction matrices that are similar to those generated by the standard method. One iteration of the s-step Arnoldi algorithm corresponds to s iterations of the standard Arnoldi algorithm. The s-step method has improved data locality, minimized global communication, and superior parallel properties. These algorithms are implemented on a 64-node NCUBE/7 Hypercube and a CRAY-2, and performance results are presented.

Approximating dominant singular triplets of large sparse matrices via modified moments

1996 ◽  
Vol 13 (1) ◽  
pp. 123-152 ◽  
Author(s):  
Sowmini Varadhan ◽  
Michael W. Berry ◽  
Gene H. Golub
Keyword(s):  
Sparse Matrices ◽  
Modified Moments ◽  
Large Sparse Matrices
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