Recently, we gave a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the Conjugate Gradient method. Roughly speaking, one may observe superlinear convergence while solving a sequence of (symmetric positive definite) linear systems if the asymptotic eigenvalue distribution of the sequence of the corresponding matrices ...

We present a new variant of the Earley parsing algorithm capable of efficiently supporting context-free grammars with regular right hand-sides. We present the core state-machine driven algorithm, the translation of grammars into state machines, and the reconstruction algorithm. We also include a theoretical framework for presenting the algorithm and for evaluating optimizations. Finally, we eva...

Unified unsymmetrical and symmetrical iterative solvers for handling multiple right-hand-side vectors are examined in this work. Efficient computer implementation strategies (to reduce computational time and in-core memory requirements) are proposed. In-core, out-of-core, linear, multiple right hand side (RHS) vectors, non-linear, symmetrical, and unsymmetrical capabilities of the developed sof...

This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely th...

In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several right-hand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have fundamental advantages over the corresponding methods for systems with a single right-hand side: much larger sear...

In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deeation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saun-ders' MINRES method for iterative solution of sym...