An efficient method for solution of systems of linear equations with many right hand sides is developed. The right hand sides are assumed to depend smoothly on a parameter. The equations are solved by an iterative method and a linear least squares approximation is used as initial guess. The work spent on the iterations is bounded independently of the number of right hand sides. The method is ap...

The sparse triangular solve kernels, SpTRSV and SpTRSM, are important building blocks for a number of numerical linear algebra routines. Parallelizing SpTRSV and SpTRSM on today’s manycore platforms, such as GPUs, is not an easy task since computing a component of the solution may depend on previously computed components, enforcing a degree of sequential processing. As a consequence, most exist...

The solution of linear systems with a parameter is an important problem in engineering applications, including structural dynamics, acoustics, and electronic circuit simulations, and in related model order reduction methods such as Padé via Lanczos. In this paper, we present a Lanczos-based method for solving parameterized symmetric linear systems with multiple right-hand sides. We show that fo...

In the present paper, we present smoothing procedures for iterative block methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These procedures generalize those known when solving one right-hand linear systems. We give some properties of these new methods and then, using these procedures we show connections between some known iterative block methods. Fina...

The technique that was used to build the eigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window...

1 Department of Computer and Information S ien e, Linköpings universitet, SE-581 83 Linköping, Sweden 2 É ole polyte hnique, Laboratoire d'informatique (LIX), 91128 Palaiseau Cedex, Fran e Abstra t. We study minimisation of integer linear programs with positive right-hand sides. We show that su h programs an be approximated within the maximum absolute row sum of the onstraint matrix A whenever ...

We introduce the bilevel knapsack problem with stochastic right-hand sides, and provide necessary and sufficient conditions for the existence of an optimal solution. When the leader’s decisions can take only integer values, we present an equivalent two-stage stochastic programming reformulation with binary recourse. We develop a branch-and-cut algorithm for solving this reformulation, and a bra...

1 Institute of Mathematics and Computer Science Academy of Sciences of Moldova Academiei 5, Chişinău, MD-2028, Moldova [email protected] 2 Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China School of Automation, Huazhong University of Science and Technology Wuhan 430074, China 3 Faculty of Informatics, TU Wien Favoritenstraße 9–11, 1040 Vienna, Au...

C06FKF Circular convolution or correlation of two real vectors, extra workspace for greater speed C06FPF Multiple one-dimensional real discrete Fourier transforms C06FQF Multiple one-dimensional Hermitian discrete Fourier transforms C06FRF Multiple one-dimensional complex discrete Fourier transforms C06FUF Two-dimensional complex discrete Fourier transform C06FXF Three-dimensional complex discr...