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In this article we test the accuracy of three platforms used in computational modelling: MatLab, Octave and Scilab, running on i386 architecture and three operating systems (Windows, Ubuntu and Mac OS). We submitted them to numerical tests…
Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…
Level-index arithmetic appeared in the 1980s. One of its principal purposes is to abolish the issues caused by underflows and overflows in floating point. However, level-index arithmetic does not expand the set of numbers but spaces out the…
Matlab is one of the most widely used mathematical computing environments in technical computing. It has an interactive environment which provides high performance computing (HPC) procedures and easy to use. Parallel computing with Matlab…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing…
A finite-difference Micromagnetic simulation code written in MATLAB is presented with Graphics Processing Unit (GPU) acceleration. The high performance of Graphics Processing Unit (GPU) is demonstrated compared to a typical Central…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resort to trial division by a few initial prime numbers, since such a division take less time. How far we should go with such a division is…
We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for…
This paper presents a MATLAB toolbox for implementing robust-to-early termination model predictive control, abbreviated as REAP, which is designed to ensure a sub-optimal yet feasible solution when MPC computations are prematurely…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…
While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Rahman and Valdman (2013) introduced a vectorized way to assemble finite element stiffness and mass matrices in MATLAB. Local element matrices are computed all at once by array operations and stored in multi-dimentional arrays (matrices).…
Pattern recognition and machine learning are becoming integral parts of algorithms in a wide range of applications. Different algorithms and approaches for machine learning include different tradeoffs between performance and computation, so…