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1: 3.8 Nonlinear Equations
Example. Wilkinsons Polynomial
2: 3.2 Linear Algebra
In the case that the orthogonality condition is replaced by S -orthogonality, that is, v j T S v k = δ j , k , j , k = 1 , 2 , , n , for some positive definite matrix S with Cholesky decomposition S = L T L , then the details change as follows. Start with v 0 = 0 , vector v 1 such that v 1 T S v 1 = 1 , α 1 = v 1 T A v 1 , β 1 = 0 . …
u = ( A - α j S ) v j - β j S v j - 1 ,
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
  • S. S. Wagstaff (1978) The irregular primes to 125000 . Math. Comp. 32 (142), pp. 583–591.
  • S. O. Warnaar (1998) A note on the trinomial analogue of Bailey’s lemma. J. Combin. Theory Ser. A 81 (1), pp. 114–118.
  • J. H. Wilkinson (1988) The Algebraic Eigenvalue Problem. Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.
  • Wolfram’s Mathworld (website)
  • C. Y. Wu (1982) A series of inequalities for Mills’s ratio. Acta Math. Sinica 25 (6), pp. 660–670.