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Graph algorithms play an important role in many computer science areas. In order to solve problems that can be modeled using graphs, it is necessary to use a data structure that can represent those graphs in an efficient manner. On top of…
This paper presents an overview of the "Applied Parallel Computing" course taught to final year Software Engineering undergraduate students in Spring 2014 at NUST, Pakistan. The main objective of the course was to introduce practical…
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 introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
Matrix functions with potential applications have a major role in science and engineering. One of the fundamental matrix functions, which is particularly important due to its connections with certain matrix differential equations and other…
Program translation refers to migrating source code from one programming language to another. It has tremendous practical value in software development, as porting software across languages is time-consuming and costly. Automating program…
Starting from the basic level of mathematica here we illustrate how to use a mathematica notebook and write a program in the notebook. Next, we investigate elaborately the way of linking of external programs with mathematica, so-called the…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
Software engineering education and training have obstacles caused by a lack of basic knowledge about a process of program execution. The article is devoted to the development of special tools that help to visualize the process. We analyze…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
We introduce program splicing, a programming methodology that aims to automate the commonly used workflow of copying, pasting, and modifying code available online. Here, the programmer starts by writing a "draft" that mixes unfinished code,…
Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…
We design a family of program analyses for JavaScript that make no approximation in matching calls with returns, exceptions with handlers, and breaks with labels. We do so by starting from an established reduction semantics for JavaScript…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
The goal of this article is to study algorithms that compute the product between two matrixes, specifically using the ingenuous methods of Strassen and Strassen-Winograd, which will be presented in Section 2. At present, the cited methods…
Mathematical expressions were generated, evaluated and used to train neural network models based on the transformer architecture. The expressions and their targets were analyzed as a character-level sequence transduction task in which the…
There are many classes of mathematical problems which give rise to matrices, where a large number of the elements are zero. In this case it makes sense to have a special matrix type to handle this class of problems where only the non-zero…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…