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Krylov methods for nonsymmetric linear systems
G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
Preconditioned krylov solvers on gpus
In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with
preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR (s) Krylov solvers. For a …
preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR (s) Krylov solvers. For a …
Combination Preconditioning and the Bramble–Pasciak Preconditioner
M Stoll, A Wathen - SIAM Journal on Matrix Analysis and Applications, 2008 - SIAM
It is widely appreciated that the iterative solution of linear systems of equations with large
sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to …
sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to …
Krylov subspace methods for linear systems
T Sogabe - Springer Series in Computational Mathematics, 2022 - Springer
In many fields of scientific computing and data science, we frequently face the problem of
solving large and sparse linear systems of the form Ax= b, which is one of the most time …
solving large and sparse linear systems of the form Ax= b, which is one of the most time …
Efficiency of General Krylov Methods on GPUs--An Experimental Study
This paper compares different Krylov methods based on short recurrences with respect to
their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS …
their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS …
The Faber–Manteuffel theorem for linear operators
A short recurrence for orthogonalizing Krylov subspace bases for a matrix A exists if and
only if the adjoint of A is a low-degree polynomial in A (ie, A is normal of low degree). In the …
only if the adjoint of A is a low-degree polynomial in A (ie, A is normal of low degree). In the …
[HTML][HTML] Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices
In inverse eigenvalue problems one tries to reconstruct a matrix, satisfying some constraints,
given some spectral information. Here, two inverse eigenvalue problems are solved. First …
given some spectral information. Here, two inverse eigenvalue problems are solved. First …
[PDF][PDF] Solving linear systems using the adjoint
M Stoll - 2008 - researchgate.net
It is widely appreciated that the iterative solution of linear systems of equations with large
sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to …
sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to …
The Bramble-Pasciak preconditioner for saddle point problems
M Stoll, A Wathen - 2007 - ora.ox.ac.uk
The Bramble-Pasciak Conjugate Gradient method is a well known tool to solve linear
systems in saddle point form. A drawback of this method in order to ensure applicability of …
systems in saddle point form. A drawback of this method in order to ensure applicability of …
When is the adjoint of a matrix a low degree rational function in the matrix?
J Liesen - SIAM journal on matrix analysis and applications, 2008 - SIAM
We show that the adjoint A^+ of a matrix A with respect to a given inner product is a rational
function in A, if and only if A is normal with respect to the inner product. We consider such …
function in A, if and only if A is normal with respect to the inner product. We consider such …