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- Mario Berljafa, Stefan GÃ¼ttel
- SIAM J. Matrix Analysis Applications
- 2015

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 and present an implicit Q theorem for rational Krylov spaces. Transformations on rational Krylov decompositions allow for changing the poles of a rational Krylovâ€¦ (More)

- Mario Berljafa, Stefan GÃ¼ttel
- SIAM J. Scientific Computing
- 2017

- Mario Berljafa, Stefan GÃ¼ttel
- SIAM J. Scientific Computing
- 2017

- Mario Berljafa, Edoardo Di Napoli
- PPAM
- 2013

In one of the most important methods in Density Functional Theory â€“ the FullPotential Linearized Augmented Plane Wave (FLAPW) method â€“ dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly correlated to the next one in the sequence. We propose a novel approach which exploits such correlation through the useâ€¦ (More)

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 continuation matrix T . Simply speaking, the j-th column of this matrix contains the coefficients of the linear combination of j rational Krylov basis vectors whichâ€¦ (More)

- MIMS EPrint, Mario Berljafa, Stefan GÃ¼ttel
- 2017

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 rational Krylov space. Typically, the computationally most expensive component of this algorithm is the solution of a large linear system of equations at eachâ€¦ (More)

- Mario Berljafa, Daniel Wortmann, Edoardo Di Napoli
- Concurrency and Computation: Practice andâ€¦
- 2015

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, some eigenproblem sequences show a connectionâ€¦ (More)

- Edoardo Di Napoli, Mario Berljafa
- Computer Physics Communications
- 2013

In Density Functional Theory simulations based on the LAPW method, each self-consistent cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct cycles have either been believed to be independent or at most very loosely connected. In a recent study [7], it was proposed toâ€¦ (More)

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