Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 November 2019Accepted: 14 July 2020Published online: 06 May 2021Keywordsinterpolation, least-squares, Vandermonde matrix, Arnoldi, polyval, polyfit, Fourier extensionAMS Subject Headings41A05, 65D05, 65D10Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200P...

We show in this text how the idea of the Implicitly Restarted Arnoldi method can be generalised to the non-symmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a Lanczos tridiagonalisation. The implicitly restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.

We introduce an overlapping time-domain decomposition for linear initial-value 7 problems which gives rise to an efficient solution method for parallel computers without 8 resorting to the frequency domain. This parallel method exploits the fact that homogeneous 9 initial-value problems can be integrated much faster than inhomogeneous problems by using 10 an efficient Arnoldi approximation for ...

We analyze the the convergence behavior of block GMRES and characterize the phenomenon of stagnation which is then related to the behavior of the block FOM method. We generalize the block FOM method to generate well-defined approximations in the case that block FOM would normally break down, and these generalized solutions are used in our analysis. This behavior is also related to the principal...

A nonlinear Rayleigh-Ritz iterative (NRRIT) method for solving nonlinear eigenvalue problems is studied in this paper. It is an extension of the nonlinear Arnoldi algorithm due to Heinrich Voss. The effienicy of the NRRIT method is demonstrated by comparing with inverse iteration methods to solve a highly nonlinear eigenvalue problem arising from finite element electromagnetic simulation in acc...

A fast exponential time integration scheme is considered for pricing European and double barrier options in jump-diffusion models. After spatial discretization, the option pricing problem is transformed into the product of a matrix exponential and a vector, while the matrix bears a Toeplitz structure. The shift-and-invert Arnoldi method is then employed for fast approximations to such operation...

In this text, we present a generalisation of the idea of the Implicitly Restarted Arnoldi method to the nonsymmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a full Lanczos tridi-agonalisation. The Implicitly Restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.

In general, the optimal computational complexity of Arnoldi iteration is O(kN) for solving a generalized eigenvalue problem, with k being the number of dominant eigenvalues and N the matrix size. In this work, we reduce the computational complexity of the Arnoldi iteration from O(kN) to O(N), thus paving the way for full-wave extraction of very large-scale onchip interconnects, the k of which i...