Wilkinson polynomial
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1: 3.8 Nonlinear Equations
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Example. Wilkinson’s Polynomial
…2: 3.2 Linear Algebra
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►The polynomial
…The multiplicity of an eigenvalue is its multiplicity as a zero of the characteristic polynomial (§3.8(i)).
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►Its characteristic polynomial can be obtained from the recursion
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►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
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Global asymptotics of the Meixner polynomials.
Asymptotic Analysis 75 (3-4), pp. 211–231.
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach.
J. Math. Pures Appl. (9) 85 (5), pp. 698–718.
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The Algebraic Eigenvalue Problem.
Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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