Related papers: On a vectorized basic linear algebra package for p…
Deep Learning (DL) developers come from different backgrounds, e.g., medicine, genomics, finance, and computer science. To create a DL model, they must learn and use high-level programming languages (e.g., Python), thus needing to handle…
A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…
We present a simple and efficient MATLAB implementation of the linear virtual element method for the three dimensional Poisson equation. The purpose of this software is primarily educational, to demonstrate how the key components of the…
Recent trends in the HPC field have introduced new CPU architectures with improved vectorization capabilities that require optimization to achieve peak performance and thus pose challenges for performance portability. The deployment of…
There are increasingly efficient data processing pipelines that work on vectors of numbers, for instance most machine learning models, or vector databases for fast similarity search. These require converting the data to numbers. While this…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the…
Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular,…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…
Dynamic arrays, also referred to as vectors, are fundamental data structures used in many programs. Modeling their semantics efficiently is crucial when reasoning about such programs. The theory of arrays is widely supported but is not…
This paper presents a Matlab toolbox to perform basic image processing and visualization tasks, particularly designed for medical image processing. The functionalities available are similar to basic functions found in other non-Matlab…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
Generative AI technology based on Large Language Models (LLM) has been developed and applied to assist or automatically generate program codes. In this paper, we evaluate the capability of existing general LLMs for Basic Linear Algebra…
Among the components contributing to particle transport, geometry navigation is an important consumer of CPU cycles. The tasks performed to get answers to "basic" queries such as locating a point within a geometry hierarchy or computing…
This paper presents the design of HELIX, an end-to-end verified code generation system with a focus on the intersection of high-performance and high-assurance numerical computing. The code generation can be fine-tuned to generate efficient…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…