Jacobi eigenvalue algorithm: Difference between revisions

Revision as of 21:39, 1 March 2011

Revision as of 01:59, 25 March 2011

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where ''s'' = sin(''θ'') and ''c'' = cos(''θ'').

AsSince they''G'' areis similarorthogonal, ''A'' and ''A''′ have the same [[Frobenius norm]] ||·||_F (the square-root sum of squares of all components), however we can choose ''θ'' such that ''A''′_''ij'' = 0, in which case ''A''′ has a larger sum of squares on the diagonal:

:<math> A'_{ij} = \cos(2\theta) A_{ij} + \tfrac{1}{2} \sin(2\theta) (A_{ii} - A_{jj}) </math>