arXiv subjects

Saeed Karimi

Publications and source records attributed to Saeed Karimi.

2 recordsLinked to original sources

arXiv2021

Fast and flexible preconditioners for solving multilinear systems

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about preconditioned Jacobi, Gauss-Seidel and SOR type iterative methods. The main results theoretically prove that the preconditioners can accelerate the convergence of iterations. Numerical examples are presented to reverify the efficiency of the proposed preconditioned methods.

math.NA↗

arXiv2021

A new block diagonal preconditioner for a class of $3\times 3$ block saddle point problems

We study the performance of a new block preconditioner for a class of $3\times3$ block saddle point problems which arise from finite element methods for solving time-dependent Maxwell equations and some other practical problems. We also estimate the lower and upper bounds of eigenvalues of the preconditioned matrix. \cred{Finally, we examine our new preconditioner to accelerate the convergence speed of the GMRES method which shows the effectiveness of the preconditioner.

math.NA↗