Deflated and augmented global Krylov subspace methods for the matrix equations

2016 ◽  
Vol 99 ◽  
pp. 137-150
Author(s):  
G. Ebadi ◽  
N. Alipour ◽  
C. Vuik
Keyword(s):  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Matrix Equations ◽  
Subspace Methods ◽  
The Matrix

Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations

2019 ◽  
Vol 62 (1-2) ◽  
pp. 157-177
Author(s):  
El. Mostafa Sadek ◽  
Abdeslem Hafid Bentbib ◽  
Lakhlifa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Matrix Equations ◽  
Subspace Methods ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations

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.

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