Bartels–Stewart algorithm: Difference between revisions

Revision as of 09:59, 16 January 2020

Revision as of 13:15, 20 January 2020

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: <math>S = V^TB^TV.</math>

The matrices <math>R</math> and <math>S</math> are block-upper triangular matrices, with squarediagonal blocks of size no<math>1 greater\times than1</math> or <math>2 \times 2</math>.

2. Set <math>F = U^TCV.</math>

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=== Simplifications and special cases ===

In the special case where <math>B=-A^T</math> and <math>C</math> is symmetric, the solution <math>X</math> will also be symmetric. This symmetry can be exploited so that <math>Y</math> is found more efficiently in step 3 of the algorithm<ref name=":0" />.

== The Hessenberg–Schur algorithm ==