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- invited-talkJuly 2024
Corrigimus, verificamus, vincimus: Ensuring algorithmic accuracy in an age of uncertainty
ISSAC '24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic ComputationPages 8–10https://doi.org/10.1145/3666000.3672621For nearly as long as it has been developing fast heuristic, approximate, and randomized algorithms, the computer algebra community has also been keen to produce methods by which we can verify accuracy and even correct a small number of errors. These ...
- research-articleJune 2024
Formalized Functional Analysis with Semilinear Maps
AbstractSemilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear and ...
- research-articleNovember 2023
Task-Based Polar Decomposition Using SLATE on Massively Parallel Systems with Hardware Accelerators
SC-W '23: Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and AnalysisPages 1680–1687https://doi.org/10.1145/3624062.3624248We investigate a new task-based implementation of the polar decomposition on massively parallel systems augmented with multiple GPUs using SLATE. We implement the iterative QR Dynamically-Weighted Halley (QDWH) algorithm, whose building blocks mainly ...
- research-articleSeptember 2023
Parallel line identification for line-implicit-solvers
AbstractLine-implicit preconditioners are well known in computational fluid dynamics (CFD) solvers and are an essential component to handle meshes with cells of very high aspect ratio (> 1000:1). Such anisotropic cells are commonly used to resolve steep ...
- research-articleSeptember 2023
Improving the performance of classical linear algebra iterative methods via hybrid parallelism
Journal of Parallel and Distributed Computing (JPDC), Volume 179, Issue Chttps://doi.org/10.1016/j.jpdc.2023.04.012AbstractWe propose fork-join and task-based hybrid implementations of four classical linear algebra iterative methods (Jacobi, Gauss–Seidel, conjugate gradient and biconjugate gradient stabilized) on CPUs as well as variations of them. This ...
Highlights- Four classical linear algebra iterative methods are hybridised on CPUs.
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- ArticleAugust 2023
Two Experiences of Including Critical Thinking in Mathematics Courses
AbstractThe current knowledge-based society in a globalizing world requires citizens to be ready for the world around them and aware of all their daily decisions, job, or life. Critical thinking is valued in the business world. It is considered one of the ...
- research-articleMay 2023
Towards rigorous understanding of neural networks via semantics-preserving transformations
International Journal on Software Tools for Technology Transfer (STTT) (STTT), Volume 25, Issue 3Pages 301–327https://doi.org/10.1007/s10009-023-00700-7AbstractIn this paper, we present an algebraic approach to the precise and global verification and explanation of Rectifier Neural Networks, a subclass of Piece-wise Linear Neural Networks (PLNNs), i.e., networks that semantically represent piece-wise ...
- research-articleMay 2023
Incremental Interval Assignment by Integer Linear Algebra with Improvements
AbstractInterval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical ...
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Highlights- Assigns intervals, number of mesh edges, on bounding curves.
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- ArticleJanuary 2023
Linear Algebraic Abduction with Partial Evaluation
AbstractLinear algebra is an ideal tool to redefine symbolic methods with the goal to achieve better scalability. In solving the abductive Horn propositional problem, the transpose of a program matrix has been exploited to develop an efficient exhaustive ...
- ArticleOctober 2022
- ArticleJune 2022
A Note on Adjoint Linear Algebra
AbstractA new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector, matrix-...
- ArticleJune 2022
Compiling Linear Algebra Expressions into Efficient Code
AbstractIn textbooks, linear algebra expressions often use indices to specify the elements of variables. This index form expressions cannot be directly translated into efficient code, since optimized linear algebra libraries and frameworks require ...
- research-articleMay 2022
A study on square root control-systems
Journal of Computational and Applied Mathematics (JCAM), Volume 406, Issue Chttps://doi.org/10.1016/j.cam.2021.113938AbstractStarting with the simplest case of an analogue square root control-system, we extend the idea to the discrete-time case and ultimately the multivariable discrete-time case. Several new results then emerge from the multivariable work. A ...
- research-articleApril 2022
Enhancing Linear Algebraic Computation of Logic Programs Using Sparse Representation
New Generation Computing (NEWG), Volume 40, Issue 1Pages 225–254https://doi.org/10.1007/s00354-021-00142-2AbstractAlgebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation to perform logical inference in large-scale ...
- research-articleMarch 2022
A GPU-accelerated adaptive FSAI preconditioner for massively parallel simulations
International Journal of High Performance Computing Applications (SAGE-HPCA), Volume 36, Issue 2Pages 153–166https://doi.org/10.1177/10943420211017188The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in the further ...
- research-articleFebruary 2022
Tools and algorithms for the construction and analysis of systems: a special issue for TACAS 2019
International Journal on Software Tools for Technology Transfer (STTT) (STTT), Volume 24, Issue 1Pages 29–31https://doi.org/10.1007/s10009-021-00642-yAbstractAutomated techniques and tools for the construction and analysis of systems are inevitable to manage the complexity of the current systems. Such techniques and tools are the subject of interest of the International Conference on Tools and ...
- research-articleJanuary 2022
- research-articleJanuary 2022
A linear-algebraic method to compute polynomial PDE conservation laws
Journal of Symbolic Computation (JOSC), Volume 108, Issue CPages 55–72https://doi.org/10.1016/j.jsc.2021.06.003AbstractWe present a method to compute polynomial conservation laws for systems of partial differential equations (PDEs). The method only relies on linear algebraic computations and is complete, in the sense it can find a basis for all ...
- research-articleApril 2022
A Web Intelligence Solution to Support Recommendations from the Web
WI-IAT '21: IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent TechnologyPages 160–167https://doi.org/10.1145/3498851.3498966Big data are everywhere. World Wide Web and social networks are examples of these big data. They have become a vast data production and consumption platform, at which threads of data evolve from multiple devices, by different human interactions, over ...