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Wilkinson polynomial


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1: 3.8 Nonlinear Equations
Example. Wilkinson’s Polynomial
2: 3.2 Linear Algebra
The polynomial …The multiplicity of an eigenvalue is its multiplicity as a zero of the characteristic polynomial3.8(i)). … … Its characteristic polynomial can be obtained from the recursion … Many methods are available for computing eigenvalues; see Golub and Van Loan (1996, Chapters 7, 8), Trefethen and Bau (1997, Chapter 5), and Wilkinson (1988, Chapters 8, 9).
3: Bibliography W
  • X.-S. Wang and R. Wong (2011) Global asymptotics of the Meixner polynomials. Asymptotic Analysis 75 (3-4), pp. 211–231.
  • X.-S. Wang and R. Wong (2012) Asymptotics of orthogonal polynomials via recurrence relations. Anal. Appl. (Singap.) 10 (2), pp. 215–235.
  • Z. Wang and R. Wong (2006) Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. J. Math. Pures Appl. (9) 85 (5), pp. 698–718.
  • J. H. Wilkinson (1988) The Algebraic Eigenvalue Problem. Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.
  • J. A. Wilson (1978) Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials. Ph.D. Thesis, University of Wisconsin, Madison, WI.