All posts under category "Computer Science / Mathematical Software"
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space complexity of dense matrix vector multiplication,
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and higher-order scalar equations where growth behavior is expressed in ter
In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical accuracy of the method.
From the discovery that the template system of C++ forms a Turing complete language in 1994, a programming technique called Template Metaprogramming has emerged that allows for the creation of faster, more generic and better code. Here, we apply Template Metaprogramming to implement a generic Runge-
Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain reasoners for doing the exercise-specific calculations. Since a d
Many problems that arise in machine learning domain deal with nonlinearity and quite often demand users to obtain global optimal solutions rather than local optimal ones. Optimization problems are inherent in machine learning algorithms and hence many methods in machine learning were inherited from
We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We dem
The present article is a sequel of the article 'Fislab the Fuzzy Inference Tool-Box for Scilab' and it represents the practical application of:'The development of the Fuzzy regulator with an input and an output in Fislab'. The article contains, besides this application, some functions to be used in
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanc
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are examined. A very brief introduction to mathematics of semirings
The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available at http://logic.csci.unt.edu/tarau/research/2008/fSET.zip .
In this work we describe an efficient implementation of a hierarchy of algorithms for Gaussian elimination upon dense matrices over the field with two elements. We discuss both well-known and new algorithms as well as our implementations in the M4RI library, which has been adopted into Sage. The foc
In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are many researches focus on finite element method with GPUs. Howe
Although, many scientists and engineers use Octave or MATLAB as their preferred programming language, dynamic nature of these languages can lead to slower running-time of programs written in these languages compared to programs written in languages which are not as dynamic, like C, C++ and Fortran.
A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. We define
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