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Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
TLDR
The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization, in particular, when using rational approximants based on the work of Zolotarev. Expand
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NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems
TLDR
A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems is proposed. Expand
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PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
TLDR
A novel parallel algorithm for the integration of linear initial-value problems is proposed based on the simple observation that homogeneous problems can typically be integrated much faster than inhomogeneous problems. Expand
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Robust Padé Approximation via SVD
TLDR
Pade approximation is considered from the point of view of robust methods of numerical linear algebra, in particular, the singular value decomposition. Expand
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Generalized Rational Krylov Decompositions with an Application to Rational Approximation
TLDR
Rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. Expand
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The nonlinear eigenvalue problem
TLDR
Nonlinear eigenvalue problems arise in a variety of science and engineering applications and in the past ten years there have been numerous breakthroughs in the development of numerical methods. Expand
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Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
TLDR
We utilize an integral representation for the error of the iterates in the Arnoldi method which allows us to develop 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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Near-Optimal Perfectly Matched Layers for Indefinite Helmholtz Problems
TLDR
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented, which converges exponentially fast in the number of grid points. Expand
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Some observations on weighted GMRES
TLDR
We investigate the convergence of the weighted GMRES method for solving linear systems. Expand
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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
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