Smooth Takagi decomp. of a complex symmetric matrix function

Numerical computation of a smooth Takagi decomposition of an n-by-n complex symmetric matrix valued function of one real parameter
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Updated 30 Apr 2025

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This function numerically computes the Takagi decomposition of an n-by-n complex symmetric matrix-valued function FUN of one real parameter. The singular values are arranged in decreasing order and are assumed to be distinct and non-zero for all values of the parameter. It is possible to continue a subset of the singular values and corresponding singular vectors.
A typical call to takagiCont is:
[Tout,Uout,Sout,flag]=takagiCont(f,tspan,params)
See the script example_takagiCont.m for an example of how to use the function.
The command "help takagiCont" displays information and functionality of the software.
Please cite the references below if you use this software.
Authors: Alessandra Papini and Alessandro Pugliese

Cite As

L. Dieci, A. Papini, A. Pugliese, "Takagi factorization of matrices depending on parameters and locating degeneracies of singular values". SIAM J. Matrix Anal. Appl., Vo. 43, Iss. 3, pp. 1148-1161, 2022. https://doi.org/10.1137/21M1456273

MATLAB Release Compatibility
Created with R2023b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.1

Fixed typos

1.0.0