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For a linear matrix function $f$ in $X \in \R^{m\times n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E \neq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions…

A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation…

The growing availability and usage of low precision foating point formats has attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. In this paper we investigate the possibility of…

This paper presents a convex optimization-based solution to the design of state-feedback controllers for solving the linear quadratic regulator (LQR) problem of uncertain discrete-time systems with multiplicative noise. To synthesize a…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our preliminary results show that the proposed algorithm applied…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…

We consider the low-rank alternating directions implicit (ADI) iteration for approximately solving large-scale algebraic Sylvester equations. Inside every iteration step of this iterative process a pair of linear systems of equations has to…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…

This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI…

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial…

We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…

Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…

We present a new, simple and computationally efficient iterative method for low rank matrix completion. Our method is inspired by the class of factorization-type iterative algorithms, but substantially differs from them in the way the…

We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…