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Asked: 2026-06-13T22:24:56+00:00

I’m using the dgesv and dgemm fortran subroutines in C++ to do some simple

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I’m using the dgesv and dgemm fortran subroutines in C++ to do some simple matrix multiplication and left division.

For random matrices A and B, I do:

A\(A\(A*B));

where * is defined using dgemm and \ using dgesv. Obviously, this expression should simplify to the identity matrix. I’m testing my answers against MATLAB and I’m getting more or less 1’s on the diagonal but the other entries are very slightly off (the numbers are on the order of magnitude e-15, so they’re close to 0 already).

I’m just wondering if this result is to be expected or not? Because if I do something like this:

C = A+B;
D = A*B;

D\(C\(C*C));

the result should come out to D\C. Basically, C(C*C) is very accurate (matches MATLAB perfectly), but the second I do D\C I get something that’s off by e-1 or even e+00. I’m guessing that’s not supposed to happen?

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1 Answer

  1. Editorial Team

    Your problem seems to be related to finite accuracy of floating point variables in C/C++. You can read more about it here. There are some techniques of minimizing that effect (some of them described in the wiki article) but there will always be some loss of accuracy after a few operations. You might want to use some third-party mathematical library that supports numbers of arbitrary precision (e.g. GMP). But still – as long as you stick to numerical approach accuracy of your calculations will always be tainted.

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