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1: 3.1 Arithmetics and Error Measures

§3.1 Arithmetics and Error Measures

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§3.1(v) Error Measures

… ►The relative precision is … ►The mollified error is … ►

2: 3.2 Linear Algebra

… ►Because of rounding errors, the residual vector $𝐫=𝐛-𝐀𝐱$ is nonzero as a rule. … ►The sensitivity of the solution vector $𝐱$ in (3.2.1) to small perturbations in the matrix $𝐀$ and the vector $𝐛$ is measured by the condition number … ►Then we have the a posteriori error bound … ►If $𝐀$ is nondefective and $\lambda$ is a simple zero of $p_n(\lambda )$, then the sensitivity of $\lambda$ to small perturbations in the matrix $𝐀$ is measured by the condition number …

3: Errata

… ►For confirmed errors, the Editors have made the corrections listed here. … ►This especially included updated information on matrix analysis, measure theory, spectral analysis, and a new section on linear second order differential operators and eigenfunction expansions. … ►The specific updates to Chapter 18 include some results for general orthogonal polynomials including quadratic transformations, uniqueness of orthogonality measure and completeness, moments, continued fractions, and some special classes of orthogonal polynomials. … ►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions. … ►

At the end of the subsection the text which originally stated “then the measure in (18.28.10) is uniquely determined” has been updated to be “then the measure in (18.28.10) is the unique orthogonality measure”.

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4: DLMF Project News

error generating summary

5: Bibliography M

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Two-point quasi-fractional approximations to the Airy function $\mathrm{Ai}(x)$ . J. Comput. Phys. 99 (2), pp. 337–340.

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Notes:

There is an error in Eq. (5): the second term in parentheses needs to be multiplied by $x$.

External Links:

ISSN 0021-9991, Document, MathReview Entry, ZentralBlatt

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1st item.

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The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators. Rocky Mountain J. Math. 21 (1), pp. 501–527.

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External Links:

ISSN 0035-7596, Document, Link, MathReview (T. S. Chihara)

Referenced by:

§18.2(xi).

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Uniform computation of the error function and other related functions. Math. Comp. 25 (114), pp. 339–344.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.22(i).

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Explicit error terms for asymptotic expansions of Stieltjes transforms. J. Inst. Math. Appl. 22 (2), pp. 129–145.

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External Links:

ISSN 0020-2932, Document, MathReview (G. M. Habibullah), ZentralBlatt

Referenced by:

§2.6(ii).

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BibTeX

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