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Perturbation Theory

In: Theory and Computation of Complex Tensors and its Applications

Author

Listed:
  • Maolin Che

    (Southwestern University of Finance and Economics, School of Economics Mathematics)

  • Yimin Wei

    (Fudan University, School of Mathematical Sciences)

Abstract

Backward errors and condition numbers Condition number are important in modern numerical linear algebra. If a numerical algorithm is backward stable, then the product of the condition number and backward error is the first order asymptotic error bound of the solution. We recommend the monographs Stewart and Sun, Golub and Van Loan, Wilknson, and Kågström and Ruhe for the background of the matrix eigenvalue problem. These consist of the matrix standard eigenvalue problem, the matrix generalized eigenvalue problem and the matrix polynomial eigenvalue problem.

Suggested Citation

  • Maolin Che & Yimin Wei, 2020. "Perturbation Theory," Springer Books, in: Theory and Computation of Complex Tensors and its Applications, chapter 0, pages 51-96, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-2059-4_3
    DOI: 10.1007/978-981-15-2059-4_3
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