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In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
This paper proposes a robust, high-precision positioning methodology to address localization failures arising from complex background interference in large-scale flight navigation and the computational inefficiency inherent in conventional…
Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable…
With the development of large-scale integrated circuits, electronic design automation~(EDA) tools are increasingly emphasizing efficiency, with parallel algorithms becoming a trend. The optimization of delay reduction is a crucial factor…
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…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…
We present a mixed-precision benchmark called HPL-MxP that uses both a lower-precision LU factorization with a non-stationary iterative refinement based on GMRES. We evaluate the numerical stability of one of the methods of generating the…
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
Division algorithms have been developed to reduce latency and to improve the efficiency of the processors. Floating point division is considered as a high latency operation. This papers looks into one such division algorithm, examines the…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…
Our goal is to design architectures that retain the groundbreaking performance of CNNs for landmark localization and at the same time are lightweight, compact and suitable for applications with limited computational resources. To this end,…
We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give algorithms with…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
A tridiagonal matrix algorithm (TDMA), Pipelined-TDMA, is developed for multi-GPU systems to resolve the scalability bottlenecks caused by the sequential structure of conventional divide-and-conquer TDMA. The proposed method pipelines…