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**public sources and our publisher partners.**Generalized rational Krylov decompositions are matrix relations which, under certain conditions, are associated with rational Krylov spaces. We study the algebraic properties of such decompositions… Continue Reading

The RKFIT algorithm outlined in [M. Berljafa and S. GA¼ttel, Generalized rational Krylov decompositions with an application to rational approximation, SIAM J. Matrix Anal. Appl., 2015] is a… Continue Reading

Numerical methods based on rational Krylov spaces have become an indispensable tool of scientific computing. In this thesis we study rational Krylov spaces by considering rational Krylov… Continue Reading

The Rational Krylov Toolbox contains MATLAB implementations of Ruhe's rational Krylov sequence method, algorithms for the implicit and explicit relocation of the poles of a rational Krylov space, and… Continue Reading

Abstract In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space… Continue Reading

In many scientific applications, the solution of nonlinear differential equations are obtained through the setup and solution of a number of successive eigenproblems. These eigenproblems can be… Continue Reading

Rational Krylov methods are applicable to a wide range of scientific computing problems, and the rational Arnoldi algorithm is a commonly used procedure for computing an orthonormal basis of a… Continue Reading

In one of the most important methods in Density Functional Theory – the Full-Potential Linearized Augmented Plane Wave (FLAPW) method – dense generalized eigenproblems are organized in long… Continue Reading

1 Rational Krylov spaces A rational Krylov space is a linear vector space of rational functions in a matrix times a vector [5]. Let A be a square matrix of size N×N , b an N×1 nonzero starting… Continue Reading

Since version 2.4 of the RKToolbox, the rat krylov function can simulate the parallel construction of a rational Krylov basis. This is done by imposing various nonzero patterns in a so-called… Continue Reading