Diagonalization of Hermitian Matrices; Maximization of Speed and Accuracy
In this paper I describe an algorithm for finding all of the eigenvalues and eigenvectors of an Hermitian matrix (either complex or real, symmetric). The algorithm is a combination of Householder reduction to tri-diagonal form and a modified QR method for obtaining both eigenvalues and eigenvectors of the reduced matrix. The central new practical technique communicated here lies in the modification of the QR method when generating eigenvectors along with the eigenvalues.
KeywordsHermitian Matrix Hermitian Matrice Eigenvector Matrix Inverse Iteration Householder Transformation
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