engleski

The high relative accuracy of the HZ method

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 (A S ) and κ2 (B S ) are small. 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.

Generalized-eigenvalue-problem ; Hari–Zimmermann-method ; High-relative-accuracy

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