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An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. (English) Zbl 0614.65043

For positive definite symmetric matrices \(A_ 1,...,A_ k(k\geq 1)\) of dimension \(p\times p\) the measure of simultaneous deviation of \(A_ 1,...,A_ k\) from diagonality is defined as the function \(\Phi (A_ 1,...,A_ k;\quad n_ 1,...,n_ k)=\prod^{k}_{i=1}[\det (diag A_ i)]^{n_ i}/[\det (A_ i)]^{n_ i}\) where \(n_ i\) are positive constants. An algorithm for finding an orthogonal \(p\times p\) matrix B such that \(\Phi (B^ TA_ 1B,...,B^ TA_ kB;n_ 1,...,n_ k)\) is minimal is described. Conditions for the uniqueness of the solution are given. For \(k=1\) the algorithm computes the eigenvectors of the positive definite symmetric matrix. Some examples are shown.
Reviewer: L.Boubeliková

MSC:

65F30 Other matrix algorithms (MSC2010)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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