Inexact Sparse Matrix Vector Multiplication in Krylov Subspace Methods: An Application-Oriented Reduction Method

2014 ◽  
pp. 534-544
Author(s):  
Ahmad Mansour ◽  
Jürgen Götze
Keyword(s):  
Krylov Subspace ◽  
Reduction Method ◽  
Sparse Matrix ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

scholarly journals A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations

2016 ◽  
Vol 9 (2) ◽  
pp. 289-314 ◽  
Author(s):  
Wujian Peng ◽  
Qun Lin
Keyword(s):  
Iterative Methods ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Coefficient Matrix ◽  
Projection Methods ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Linear System Of Equations ◽  
Matrix Vector Multiplication ◽  
The Matrix

AbstractMost current prevalent iterative methods can be classified into the socalled extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional Krylov subspace methods which always depend on the matrix-vector multiplication with a fixed matrix, the newly introduced methods (the so-called (progressively) accumulated projection methods, or AP (PAP) for short) use a projection matrix which varies in every iteration to form a subspace from which an approximate solution is sought. More importantly an accelerative approach (called APAP) is introduced to improve the convergence of PAP method. Numerical experiments demonstrate some surprisingly improved convergence behavior. Comparison between benchmark extended Krylov subspace methods (Block Jacobi and GMRES) are made and one can also see remarkable advantage of APAP in some examples. APAP is also used to solve systems with extremely ill-conditioned coefficient matrix (the Hilbert matrix) and numerical experiments shows that it can bring very satisfactory results even when the size of system is up to a few thousands.

scholarly journals Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces

2021 ◽  
Author(s):  
Yuka Hashimoto ◽  
Takashi Nodera
Keyword(s):  
Krylov Subspace ◽  
Time Series Data ◽  
Linear Equations ◽  
Transfer Operator ◽  
Krylov Subspace Methods ◽  
Krylov Subspace Method ◽  
Linear Operators ◽  
Series Data ◽  
Subspace Method ◽  
Subspace Methods

AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.

scholarly journals Sparse Matrix-Vector Multiplication on GPGPUs

2017 ◽  
Vol 43 (4) ◽  
pp. 1-49 ◽  
Author(s):  
Salvatore Filippone ◽  
Valeria Cardellini ◽  
Davide Barbieri ◽  
Alessandro Fanfarillo
Keyword(s):  
Sparse Matrix ◽  
Matrix Vector Multiplication ◽  
Matrix Vector
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