Tag Archives: MATLAB

Randsvd Matrices with Large Growth Factors

Sixty years ago James Wilkinson published his backward error analysis of Gaussian elimination for solving a linear system , where is a nonsingular matrix. He showed that in floating-point arithmetic the computed solution satisfies where is the unit roundoff and … Continue reading

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Simulating Low Precision Floating-Point Arithmetics in MATLAB

At least five floating-point arithmetics are available in mainstream hardware: the IEEE double precision (fp64), single precision (fp32), and half precision (fp16) formats, bfloat16, and tf32, introduced in the recently announced NVIDIA A100, which uses the NVIDIA Ampere GPU architecture. … Continue reading

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Singular Values of Rank-1 Perturbations of an Orthogonal Matrix

What effect does a rank-1 perturbation of norm 1 to an orthogonal matrix have on the extremal singular values of the matrix? Here, and throughout this post, the norm is the 2-norm. The largest singular value of the perturbed matrix … Continue reading

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Update of Catalogue of Software for Matrix Functions

Edvin Hopkins and I have updated to version 3.0 the catalogue of software for matrix functions that we originally produced in 2014 and updated in 2016. It covers what is available in various languages (C++, Fortran, Java, Julia, Python, Rust), … Continue reading

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What’s New in MATLAB R2019a and R2019b?

I didn’t have time earlier this year to write about the first MATLAB release of 2019, so in this post I will discuss R2019a and R2019b together. As usual in this series, I concentrate on the features most relevant to … Continue reading

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What’s New in MATLAB R2018b?

The MATLAB R2018b release notes report a number of performance improvements, including faster startup and faster calls to built-in functions. I pick out here a few other highlights from the release (excluding the toolboxes) that are of interest from the … Continue reading

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What’s New in MATLAB R2018a?

MATLAB R2018a was released in March 2018. With each biannual release I try to give a brief overview of the changes in MATLAB (not the toolboxes) that are of most interest to me. These are not comprehensive summaries of what’s … Continue reading

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The Strange Case of the Determinant of a Matrix of 1s and -1s

By Nick Higham and Alan Edelman (MIT) In a 2005 talk the second author noted that the MATLAB det function returns an odd integer for a certain 27-by-27 matrix composed of s and s: >> A = edelman; % Set … Continue reading

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What’s New in MATLAB R2017b?

Following my earlier posts What’s New in MATLAB R2016b? and What’s New in MATLAB R2017a? I take a look here at the R2017b release of MATLAB. As before, this is not a comprehensive treatment (for which see the Release Notes), … Continue reading

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How Fast is Quadruple Precision Arithmetic?

When I am testing an algorithm running in double precision arithmetic I often want to compare the computed solution with a reference solution: a solution that is fully accurate to double precision. To obtain one I solve the same problem … Continue reading

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