lanczos-type algorithms are well known for their inherent instability. they typically breakdown occurs when relevant orthogonal polynomials do not exist. current approaches to curing breakdown rely on jumping over the non-existent polynomials to resume computation. this may have to be used many times during the solution process. we suggest an alternative to jumping, which consists of restarting...

In the present thesis we introduce several ways of extending restarting automata to devices for realizing binary (word) relations, which is mainly motivated by linguistics. In particular, we adapt the notion of input/output-relations and proper-relations to restarting automata and to parallel communicating systems of two restarting automata (PC-systems). Further, we introduce a new model, calle...

Krylov eigensolvers are used in many scientific fields, such as nuclear physics, page ranking, oil and gas exploration, etc... In this paper, we focus on the ERAM Krylov eigensolver whose convergence is strongly correlated to the Krylov subspace size and the restarting vector v0, a unit norm vector. We focus on computing the restarting vector v0 to accelerate the ERAM convergence. First, we stu...

In the literature various notions of (non-) monotonicity of restarting automata have been studied. Here we introduce two new variants of (non-) monotonicity for restarting automata and for two-way restarting automata: left (non-) monotonicity and right-left (non-) monotonicity. It is shown that for the various types of deterministic and nondeterministic (two-way) restarting automata without aux...

The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired. We analyze several approaches to restarting and show why Sorensen’s implicit QR approach is g...

The stateless deterministic ordered restarting automata accept exactly the regular languages, and it is known that the trade-off for turning a stateless deterministic ordered restarting automaton into an equivalent DFA is at least double exponential. Here we present a construction that yields an equivalent NFA of size 2 from a stateless deterministic ordered restarting automaton that works on a...

In this paper we present a study of four generic strategies for solving constraint satisfaction problems (CSPs) of any kind, be they soluble or insoluble. All four methods combine learning with restarting, two use a fixed cutoff restarting strategy followed by a run to completion, the other two use universal restarting strategies where the cutoff varies from run to run. Learning takes the form ...

We introduce a new mode of operation for CD-systems of restarting automata by providing explicit enable and disable conditions in the form of regular constraints. We show that, for each CD-systemM of restarting automata and each mode m of operation considered by Messerschmidt and Otto, there exists a CD-systemM′ of restarting automata of the same type asM that, working in the new mode ed, accep...