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HenrikSchumacher / DPR1Eigensystem

A Mathematica implementation of an eigensolver for symmetric, positive-definite rank-one modifications of diagonal matrices.
MIT License
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DPR1Eigensystem

A Mathematica implementation of an eigensolver for symmetric, positive-definite rank-one modifications of diagonal matrices.

Derived from the following paper: https://doi.org/10.1016/j.laa.2015.09.025

Installation and usage

Simply copy the file DPR1Eigensystem.m anywhere, where Mathematica can find it, e.g., unto the path

 FileNameJoin[{$BaseDirectory, "Applications"}]

Run PR1Eigensystem`* to see the packages contents. The main routine is just called DPR1Eigensystem. Run ?DPR1Eigensystem to get its syntax information.

Also see

https://mathematica.stackexchange.com/a/280669/38178
https://mathematica.stackexchange.com/a/280683/38178

for context and usage examples.

Disclaimer

All this is done under the assumption that no two elements of diag coincide. The Cauchy interlacing theorem implies that no eigenvalue has a multiplicity. Not sure how to deal with multiplicities...