Related papers: Development of a Java Package for Matrix Programmi…

In recent years it has been shown that for many linear algebra operations it is possible to create families of algorithms following a very systematic procedure. We do not refer to the fine tuning of a known algorithm, but to a methodology…

Processes to automate the selection of appropriate algorithms for various matrix computations are described. In particular, processes to check for, and certify, various matrix properties of black box matrices are presented. These include…

Pattern languages are well-established in the software architecture community. Many different aspects of creating a software architecture are addressed by such languages. Thus, several pattern languages have to be considered when building a…

Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…

A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…

We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…

Power ISA(TM) Version 3.1 has introduced a new family of matrix math instructions, collectively known as the Matrix-Multiply Assist (MMA) facility. The instructions in this facility implement numerical linear algebra operations on small…

Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…

The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…

In order to precondition Toeplitz systems, we present a new class of simultaneously diagonalizable real matrices, the Gamma-matrices, which include both symmetric circulant matrices and a subclass of the set of all reverse circulant…

Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…

The explosion of Big Data was followed by the proliferation of numerous complex parallel software stacks whose aim is to tackle the challenges of data deluge. A drawback of a such multi-layered hierarchical deployment is the inability to…

Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…

We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…

Arrays are such a rich and fundamental data type that they tend to be built into a language, either in the compiler or in a large low-level library. Defining this functionality at the user level instead provides greater flexibility for…

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

We describe how to use refactoring tools to transform a Java program conforming to the Composite design pattern into a program conforming to the Visitor design pattern with the same external behavior. We also describe the inverse…

This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…