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How good are MatLab, Octave and Scilab for computational modelling? (English) Zbl 1261.65007

Summary: 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 using standard data sets and using the functions provided by each platform. A Monte Carlo study was conducted in some of the datasets in order to verify the stability of the results with respect to small departures from the original input. We propose a set of operations which include the computation of matrix determinants and eigenvalues, whose results are known. We also used data provided by NIST (National Institute of Standards and Technology), a protocol which includes the computation of basic univariate statistics (mean, standard deviation and first-lag correlation), linear regression and extremes of probability distributions. The assessment was made comparing the results computed by the platforms with certified values, that is, known results, computing the number of correct significant digits.

MSC:

65C20 Probabilistic models, generic numerical methods in probability and statistics
65C05 Monte Carlo methods
65C60 Computational problems in statistics (MSC2010)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F40 Numerical computation of determinants
62J05 Linear regression; mixed models
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