A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
Filters
A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers
2015
Journal of Computational Physics
Preserved Fulltext
Other Versions
We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently ...
We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series ...
We would also like to thank James Lambers and Anil Damle for their careful reading of the manuscript and useful suggestions. ...
doi:10.1016/j.jcp.2015.07.007
fatcat:supyau6px5b4zlshklyqqko7hi
An improved Krylov eigenvalue strategy using the FEAST algorithm with inexact system solves
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour integration in the complex plane to obtain the eigenvectors of a matrix for the eigenvalues that are located in any user-defined ...
We show that this iterative FEAST algorithm (which we call IFEAST) is mathematically equivalent to a block Krylov subspace method for solving eigenvalue problems. ...
This material is supported by Intel and NSF under Grant #CCF-1510010. ...
arXiv:1706.00692v1
fatcat:whvqv36zprfijjsmfbif6qsopq
Comparison of Numerical Methods and Open-Source Libraries for Eigenvalue Analysis of Large-Scale Power Systems
2020
Applied Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
These kinds of eigenvalue problems are particularly difficult for most numerical methods to handle. ...
The paper focuses, in particular, on methods and software libraries that are able to handle the large-scale, non-symmetric matrices that arise in power system eigenvalue problems. ...
the following classes of eigenvalue numerical methods: vector iteration methods, Schur decomposition methods, Krylov subspace methods, and contour integration methods. ...
doi:10.3390/app10217592
fatcat:twyqzug2j5c3jhroisuq4uidae
Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation
2018
Journal of Computational Physics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Existing methods The existing approaches to solve a general nonlinear eigenvalue problem can, roughly speaking, be grouped into three main classes [38] : Newton-based techniques, contour integration methods ...
, the rational linearization method [34] , the infinite Arnoldi method [15] , the Newton rational Krylov method [38] , the fully rational Krylov method [14] , and the generic class of CORK methods ...
doi:10.1016/j.jcp.2018.08.017
fatcat:sartf4mhkjhancou7i67zbextm
Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector
2018
SIAM Journal on Matrix Analysis and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
On the other hand, we adapt several existing Krylov subspace techniques to the computation of the weighted geometric mean. ...
We derive two novel algorithms, based on Gauss-Jacobi quadrature, and tailor an existing technique based on contour integration. ...
, and Mario Berljafa, for fruitful discussions about the RKFIT algorithm and the use of the Rational Krylov Toolbox. ...
doi:10.1137/16m1073315
fatcat:qa66qkm3h5gafc5t4emkjkzyki
A rational QZ method
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Whereas the QZ method performs nested subspace iteration driven by a polynomial, the rational QZ method allows for nested subspace iteration driven by a rational function, this creates the additional freedom ...
The link with rational Krylov subspaces allows us to prove essential uniqueness (implicit Q theorem) of the rational QZ iterates as well as convergence of the proposed method. ...
This approach is inspired by the link between contour integration methods [17, 22] and rational filtering techniques [24, 25] . ...
arXiv:1802.04094v2
fatcat:4xk5f4ntjfhyhpfakvs7hodbx4
Solving stochastic chemical kinetics by Metropolis Hastings sampling
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
algorithm to accelerate the accuracy of the tau-leap method. ...
Samples generated by this technique have the same distribution as SSA and the histogram of samples show it's convergence to SSA. ...
Acknowledgements This work was partially supported by awards NSF DMS-1419003, NSF CCF-1218454, AFOSR FA9550-12-1-0293-DEF, AFOSR 12-2640-06, and by the Computational Science Laboratory at Virginia Tech ...
arXiv:1410.8155v1
fatcat:bx5unzt2orempgyey5pfrx4oju
Deflated Restarting for Matrix Functions
2011
SIAM Journal on Matrix Analysis and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We investigate an acceleration technique for restarted Krylov subspace methods for computing the action of a function of a large sparse matrix on a vector. ...
An approximation to the subspace to be deflated is successively refined in the course of the underlying restarted Arnoldi process by extracting Ritz vectors and using those closest to the spectral region ...
Methods based on rational Krylov spaces (cf. ...
doi:10.1137/090774665
fatcat:thqryhld3vawla62zwsrepzzvm
Limited-memory polynomial methods for large-scale matrix functions
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We review various limited-memory methods for the approximation of the action of a large-scale matrix function on a vector. ...
Methods based on explicit polynomial approximation or interpolation, as well as restarted Arnoldi methods, are treated in detail. ...
Parts of this survey were prepared during visits of the last two authors to the Department of Mathematics at The University of Manchester, whose hospitality is gratefully acknowledged. ...
arXiv:2002.01682v3
fatcat:4m7lsekh4vhyxodkrxcapxmui4
Time Integration and Steady-State Continuation for 2d Lubrication Equations
2010
SIAM Journal on Applied Dynamical Systems
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2011; you can also visit the original URL.
The file type is application/pdf.
Other Versions
On the other hand, we consider the depinning of drops pinned by a wettability defect. ...
In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. ...
We thank the Max-Planck-Institut für Physik komplexer Systeme in Dresden (Germany) that hosted us during the early stage of the project. P. B. is also grateful to L. S. ...
doi:10.1137/080718619
fatcat:qgxfyveodrhgjnlk4ey7bhlz34
A map of contour integral-based eigensolvers for solving generalized eigenvalue problems
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
From the analysis, we conclude that all contour integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem ...
In this paper, we reconsider the algorithms of the five typical contour integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. ...
Kensuke Aishima, The University of Tokyo for his valuable comments. The authors are also grateful to an anonymous referee for useful comments. ...
arXiv:1510.02572v2
fatcat:fcqzcfzylfhuvhzxnsv6vv7s4e
Beyond AMLS: Domain decomposition with rational filtering
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Compared to rational filtering projection methods applied to the original matrix pencil, the proposed technique integrates only a part of the matrix resolvent while it applies any orthogonalization necessary ...
Numerical experiments performed in distributed memory architectures illustrate the competitiveness of the proposed technique against rational filtering Krylov approaches. ...
To reduce the orthonormalization and memory costs, it is typical to enhance the convergence rate of the Krylov projection method of choice by a filtering acceleration technique so that eigenvalues located ...
arXiv:1711.09487v1
fatcat:pkp2pkms3bd3xptpxkuavpn4oq
Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Our method combines Krylov subspace methods with a rational approximation and typically achieves 4 decimal places of accuracy with fewer than 100 MVMs. ...
We demonstrate our method's applicability on matrices as large as 50,000 × 50,000 - well beyond traditional methods - with little approximation error. ...
Acknowledgments and Disclosure of Funding ...
arXiv:2006.11267v2
fatcat:twbpjfca2nc5npww4q442itdoq
Approximation of functions of large matrices with Kronecker structure
2016
Numerische Mathematik
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
Our findings are illustrated by numerical experiments with typical functions used in applications. ...
of the problem and for many ways of numerically approximating its solution. ...
Rational Krylov subspace approximation. ...
doi:10.1007/s00211-016-0799-9
fatcat:rnidatkf3bcopmdny6ev66kgme
Approximation of functions of large matrices with Kronecker structure
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Our findings are illustrated by numerical experiments with typical functions used in applications. ...
We consider the numerical approximation of f( A)b where b∈ R^N and A is the sum of Kronecker products, that is A=M_2 ⊗ I + I ⊗ M_1∈ R^N× N. ...
Rational Krylov subspace approximation. ...
arXiv:1503.02615v1
fatcat:agko7bdxgnhbrfnvquc2qkqlsq
« Previous
Showing results 1 — 15 out of 179 results