Wilkinson’s

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2: 3.2 Linear Algebra
In the case that the orthogonality condition is replaced by $\mathbf{S}$-orthogonality, that is, $\mathbf{v}_{j}^{\rm T}\mathbf{S}\mathbf{v}_{k}=\delta_{j,k}$, $j,k=1,2,\ldots,n$, for some positive definite matrix $\mathbf{S}$ with Cholesky decomposition $\mathbf{S}=\mathbf{L}^{\rm T}\mathbf{L}$, then the details change as follows. Start with $\mathbf{v}_{0}=\boldsymbol{{0}}$, vector $\mathbf{v}_{1}$ such that $\mathbf{v}_{1}^{\rm T}\mathbf{S}\mathbf{v}_{1}=1$, $\alpha_{1}=\mathbf{v}_{1}^{\rm T}\mathbf{A}\mathbf{v}_{1}$, $\beta_{1}=0$. …
$\mathbf{u}=\left(\mathbf{A}-\alpha_{j}\mathbf{S}\right)\mathbf{v}_{j}-\beta_{j% }\mathbf{S}\mathbf{v}_{j-1},$
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.