Jacobi eigenvalue algorithm: Difference between revisions

Revision as of 21:53, 6 December 2024

Revision as of 21:55, 6 December 2024

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Since singular values of a real matrix are the square roots of the eigenvalues of the symmetric matrix <math> S = A^T A</math> it can also be used for the calculation of these values. For this case, the method is modified in such a way that ''S'' must not be explicitly calculated which reduces the danger of [[round-off error]]s. Note that <math> J S J^T = J A^T A J^T = J A^T J^T J A J^T = B^T B </math> with <math> B \, := J A J^T </math> .

The Jacobi Method is also well suited for parallelism.{{fact|date=November 2024|reason=The only obvious opportunities for parallelisation seem to be within the individual Jacobi rotations, and those are very small chunks of work, for a linear algebra algorithm. "well suited" thus feels like a hyperbole.}}

== References ==