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Neat Randomized Algorithms: RandDiag for Rapidly Diagonalizing Normal Matrices
Consider two complex-valued square matrices and . The first matrix is Hermitian, being equal to its conjugate transpose .
Let’s see how long it takes MATLAB to compute the eigenvalue decomposition of a unitary (and thus normal) matrix: He and Kressner developed a beautifully simple randomized algorithm called RandDiag to circumvent this failure mode. (It would take a very special circumstances for a random linear combination to yield two eigenvalues that are exactly the same!)
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