Wilkinson’s

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1: 3.8 Nonlinear Equations

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Example. Wilkinson’s Polynomial

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2: 3.2 Linear Algebra

… ►In the case that the orthogonality condition is replaced by $𝐒$-orthogonality, that is, ${𝐯}_j^{\mathrm{T}}𝐒{𝐯}_k={\delta }_{j,k}$, $j,k=1,2,\mathrm{\dots },n$, for some positive definite matrix $𝐒$ with Cholesky decomposition $𝐒={𝐋}^{\mathrm{T}}𝐋$, then the details change as follows. Start with ${𝐯}_0=\mathrm{𝟎}$, vector ${𝐯}_1$ such that ${𝐯}_1^{\mathrm{T}}𝐒{𝐯}_1=1$, ${\alpha }_1={𝐯}_1^{\mathrm{T}}𝐀{𝐯}_1$, ${\beta }_1=0$. … ►

$𝐮=\left(𝐀-{\alpha }_j𝐒\right){𝐯}_j-{\beta }_j𝐒{𝐯}_{j-1},$

… ►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

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The irregular primes to $125000$ . Math. Comp. 32 (142), pp. 583–591.

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External Links:

FullText, Document, MathReview (Wells Johnson), ZentralBlatt

Referenced by:

§24.20.

Encodings:

BibTeX

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A note on the trinomial analogue of Bailey’s lemma. J. Combin. Theory Ser. A 81 (1), pp. 114–118.

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External Links:

ISSN 0097-3165, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX

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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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Notes:

Paperback reprint of original edition, published in 1965 by Clarendon Press, Oxford.

External Links:

ISBN 0-19-853418-3, MathReview, ZentralBlatt

Referenced by:

§3.2(v), §3.2(vi), §3.2(vii).

Encodings:

BibTeX

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Notes:

A free resource from Wolfram Research built with Mathematica technology.

External Links:

Home Page

Referenced by:

8th item, § ‣ Software Cross Index.

Encodings:

BibTeX

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A series of inequalities for Mills’s ratio. Acta Math. Sinica 25 (6), pp. 660–670.

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External Links:

MathReview (J. S. Huang), ZentralBlatt

Referenced by:

§7.8.

Encodings:

BibTeX

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