A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

In this paper an interesting property of the restarted FOM algorithm for solving large nonsymmetric linear systems is presented and studied. By establishing a relationship between the convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown that some important information of previous FOM(m) cycles may be saved by the iteration approximates at ...

We introduce two new models of two-dimensional computing devices called sgraffito automaton and restarting tiling automaton. The models fulfill two conditions. Firstly, they do not exceed the power of finite-state automata when working over one-dimensional inputs. And secondly, they allow a clear design of important computations. We study properties of the induced families of picture languages....

Clearing and subword-clearing restarting automata are linguistically motivated models of automata. We investigate the problem of grammatical inference for such automata based on the given set of positive and negative samples. We show that it is possible to identify these models in the limit. In this way we can learn a large class of languages. On the other hand, we prove that the task of findin...

It is known that cooperating distributed systems (CD-systems) of stateless deterministic restarting automata with window size 1 accept a class of semi-linear languages that properly includes all rational trace languages. Although the component automata of such a CD-system are all deterministic, the CD-system itself is not, as in each of its computations, the initial component and the successor ...

The Explicitly Restarted Arnoldi Method (ERAM) allows to find a few eigenpairs of a large sparse matrix. The Multiple Explicitly Restarted Arnoldi Method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its convergence [3]. The MERAM allows to update the restarting vector of an ERAM by taking the interesting eigen-information obtained by the other ones into accoun...

Krylov subspace methods have proved effective for many non-Hermitian eigenvalue problems, yet the analysis of such algorithms is involved. Convergence can be characterized by the angle the approximating subspace forms with a desired invariant subspace, resulting in a geometric framework that is robust to eigenvalue ill-conditioning. This paper describes a new bound on this angle that handles th...

We consider the optimal control of an unreliable manufacturing system with restarting costs. In 1986 and 1988, Akella and Kumar (for the in nite horizon discounted cost) and Bielecki and Kumar (for the in nite horizon average expected cost) show that the optimal policy is given by an optimal inventory level (“hedging point policy”). Inspired by these simple systems, we explore a new class of mo...