engleski

Accurate eigenvalue decomposition of rank-one modifications of diagonal matrices

We present an algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with high relative accuracy in O(n) operations. The algorithm is based on a shift-and-invert approach. Only a single element of the inverse of the shifted matrix eventually needs to be computed with double the working precision.Each eigenvalue and the corresponding eigenvector can be computed separately, which makes the algorithm adaptable for parallel computing.

eigenvalue problem, rank-one modification of a diagonal matrix

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