Iterative solution of large linear systems with non-smooth submatrices using partial wavelet transforms and split-matrix matrix–vector multiplication

2003 ◽  
Vol 59 (4) ◽  
pp. 457-473 ◽  
Author(s):  
Patricia González ◽  
José C. Cabaleiro ◽  
Tomás F. Pena
Keyword(s):  
Linear Systems ◽  
Wavelet Transforms ◽  
Iterative Solution ◽  
Matrix Vector Multiplication ◽  
Matrix Vector ◽  
Large Linear Systems

Vector Monte Carlo stochastic matrix-based algorithms for large linear systems

2016 ◽  
Vol 22 (3) ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Linear Systems ◽  
Search Strategy ◽  
Stochastic Matrix ◽  
Stochastic Methods ◽  
Vector Representation ◽  
Stochastic Matrices ◽  
Short Article ◽  
Gradient Based ◽  
Matrix Vector ◽  
Large Linear Systems

AbstractIn this short article we suggest randomized scalable stochastic matrix-based algorithms for large linear systems. The idea behind these stochastic methods is a randomized vector representation of matrix iterations. In addition, to minimize the variance, it is suggested to use stochastic and double stochastic matrices for efficient randomized calculation of matrix iterations and a random gradient based search strategy. The iterations are performed by sampling random rows and columns only, thus avoiding not only matrix matrix but also matrix vector multiplications. Further improvements of the methods can be obtained through projections by a random gaussian matrix.

Iterative solution of linear systems

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 57-100 ◽  
Author(s):  
Roland W. Freund ◽  
Gene H. Golub ◽  
Noël M. Nachtigal
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Conjugate Gradient ◽  
Krylov Subspace ◽  
Iterative Solution ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Recent Advances ◽  
Gradient Type ◽  
Large Linear Systems

Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.

Iterative Solution of Large Linear Systems

1973 ◽  
Vol 27 (124) ◽  
pp. 1001
Author(s):  
Olof Widlund ◽  
David M. Young
Keyword(s):  
Linear Systems ◽  
Iterative Solution ◽  
Large Linear Systems

Iterative Solution of Large Linear Systems.

1973 ◽  
Vol 80 (1) ◽  
pp. 92
Author(s):  
L. A. Hageman ◽  
David M. Young
Keyword(s):  
Linear Systems ◽  
Iterative Solution ◽  
Large Linear Systems

A negabinary encoded matrix - vector multiplication for wavelet transforms

1997 ◽  
Vol 28 (2) ◽  
pp. 66-69
Author(s):  
Xiaona Yan ◽  
Ning Wang ◽  
Yaozu Yin ◽  
Liren Liu ◽  
Guoqiang Li
Keyword(s):  
Wavelet Transforms ◽  
Matrix Vector Multiplication ◽  
Matrix Vector
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