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The high relative accuracy of the HZ method

Author

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  • Matejaš, Josip
  • Hari, Vjeran

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.

Suggested Citation

  • Matejaš, Josip & Hari, Vjeran, 2022. "The high relative accuracy of the HZ method," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004325
    DOI: 10.1016/j.amc.2022.127358
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