How can I go about performing multi-complex arithmetic in MATLAB?
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I don't know about any built-in commands, but, I could derive a matrix representation that you could build in matlab if interested. – James S. Cook Feb 27 '15 at 20:12
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Are multicomplex number at all related to hypercomplex numbers? – horchler Feb 27 '15 at 21:25
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@JamesS.Cook: I actually just found one myself (see answer below), thanks though! – user541686 Feb 27 '15 at 21:47
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@horchler: They are a different generalization of complex numbers, so I imagine implementing multicomplex numbers and hypercomplex numbers in MATLAB will be very similar but obviously not the same. – user541686 Feb 27 '15 at 21:48
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I should talk to you more about what you are doing... let me digest that paper a bit. – James S. Cook Feb 27 '15 at 21:54
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@JamesS.Cook: Sure. It's a method for numerically stable differentiation; it just says that $f'(x) = \lim_{h \to 0} \Im{f(x + ih)} / h$ for analytic $f: \mathbb{R} \to \mathbb{R}$, and it generalizes that to higher-order derivatives. – user541686 Feb 27 '15 at 21:56
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Sounds like this for the basic case. Examples. – horchler Feb 27 '15 at 22:01
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@horchler: Yeah, that's where I became familiar with it. – user541686 Feb 27 '15 at 22:11
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@horchler It is not clear how to work with multicomplex numbers. How to extract imaginary parts from them. This works a little differently than just $imag()$ – dtn Aug 08 '22 at 15:52
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I actually found an implementation in this paper:
Computation of higher-order derivatives using the multi-complex
step method
The paper describes everything in detail, but the overall idea is to make a classdef.
user541686
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