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I am looking for an approximate diagonalization method. I need method which can generate orthogonal transformation to reduce off diagonal elements, but not necessarily make them zero. my option right now is Jacoby, but then looking for other options.

If you know of one, can you direct me to article/resource? thank you

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You might consider iterative and black-box methods, and particularly Arnoldi.

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You might consider the "QR algorithm": given A, factor A as QR (Q orthogonal and R triangular), then let A' = RQ. Repeat with A' as the new A, ad infinitum.

In a way, though, all implementable diagonalization algorithms are approximate, since it's impossible to diagonalize a general matrix in a finite number of elementary operations.

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