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Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
TLDR
This work proposes improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximation based on the work of Zolotarev, and improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel. Expand
NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems
TLDR
It is shown that NLEIGS has a computational cost comparable to the Newton rational Krylov method but converges more reliably, in particular, if the nonlinear operator has singularities nearby the target set, and it features low-rank approximation techniques for increased computational efficiency. Expand
Rational Krylov Methods for Operator Functions
TLDR
A unified and self-contained treatment of rational Krylov methods for approximating the product of a function of a linear operator with a vector and a heuristic explanation of superlinear convergence effects observed with the Rayleigh�Ritz method. Expand
PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
A novel parallel algorithm for the integration of linear initial-value problems is proposed. This algorithm is based on the simple observation that homogeneous problems can typically be integratedExpand
Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods forExpand
Generalized Rational Krylov Decompositions with an Application to Rational Approximation
TLDR
A rational Krylov method for rational least squares fitting is developed and an implicit Q theorem forrational Krylov spaces is presented. Expand
Robust Padé Approximation via SVD
TLDR
The success of this algorithm suggests that there might be variants of Pade approximation that are pointwise convergent as the degrees of the numerator and denominator increase to $\infty$, unlike traditional Pade approximants, which converge only in measure or capacity. Expand
The nonlinear eigenvalue problem *
TLDR
This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques. Expand
Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods
A computational method is given for solving the forward modeling problem for transient electromagnetic exploration. Its key features are discretization of the quasi-static Maxwell's equations inExpand
Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
TLDR
An integral representation for the error of the iterates in the Arnoldi method is utilized which allows for an efficient quadrature-based restarting algorithm suitable for a large class of functions, including the so-called Stieltjes functions and the exponential function. Expand
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