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Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity…
The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
The exponential of block triangular matrices arises in a wide range of scientific computing applications, including exponential integrators for solving systems of ordinary differential equations, Hamiltonian systems in control theory,…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…