Abstract
The high relative accuracy of the Hari–Zimmermann method for solving the generalized eigenvalue problem Ax=λBx has been proved for a set of well-behaved pairs of real symmetric positive definite matrices. These are pairs of matrices (A,B) such that the spectral conditions κ2(AS) and κ2(BS) are small, where AS=DA−1/2ADA−1/2, BS=DB−1/2BDB−1/2 and DA=diag(A), DB=diag(B). The proof is made for one step of the method. It uses a very detailed error analysis and shows that the method computes the eigenvalues of the problem to high relative accuracy. Numerical tests agree with the obtained theoretical results.
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