The paper deals with infinite block matrices having compact off diagonal parts. Bounds for the spectrum are established and estimates for the norm of the resolvent are proposed. Applications to matrix integral operators are also discussed. The main tool is the π-triangular operators defined in the paper.

The paper deals with infinite block matrices having compact off diagonal parts. Bounds for the spectrum are established and estimates for the norm of the resolvent are proposed. Applications to matrix integral operators are also discussed. The main tool is the π-triangular operators defined in the paper.

In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.

An algorithm is proposed for computing primary matrix Lambert W functions of a square matrix A, which are solutions of the matrix equation WeW = A. The algorithm employs the Schur decomposition and blocks the triangular form in such a way that Newton’s method can be used on each diagonal block, with a starting matrix depending on the block. A natural simplification of Newton’s method for the La...

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second-order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. The preconditioned conjugate gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the finite eleme...

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. The Preconditioned Conjugate Gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the Finite Eleme...

We study a weakly over-penalized symmetric interior penalty method for the biharmonic problem that is intrinsically parallel. Both a priori error analysis and a posteriori error analysis are carried out. The performance of the method is illustrated by numerical experiments. 1. Introduction. Recently, it was noted in [9] that the Poisson problem can be solved by a weakly over-penalized symmetric...

We investigate the cost of preconditioning when solving large sparse saddlepoint linear systems with Krylov subspace methods. To use the block structure of the original matrix, we apply one of two block preconditioners. Algebraic eigenvalue analysis is given for a particular case of the preconditioners. We also give eigenvalue bounds for the preconditioned matrix when the preconditioner is bloc...

Generalized Jacobi (GJ) diagonal preconditioner coupled with symmetric quasi-minimal residual (SQMR) method has been demonstrated to be efficient for solving the 2 · 2 block linear system of equations arising from discretized Biot s consolidation equations. However, one may further improve the performance by employing a more sophisticated non-diagonal preconditioner. This paper proposes to empl...