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41: 3.6 Linear Difference Equations

… ►Unless exact arithmetic is being used, however, each step of the calculation introduces rounding errors. … ►Suppose again that $f_0\ne 0$, $w_0$ is given, and we wish to calculate $w_1,w_2,\mathrm{\dots },w_M$ to a prescribed relative accuracy $ϵ$ for a given value of $M$. …

42: Bibliography O

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On the calculation of Stokes multipliers for linear differential equations of the second order. Methods Appl. Anal. 2 (3), pp. 348–367.

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External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.7(ii).

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BibTeX

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43: 3.10 Continued Fractions

… ►For several special functions the $S$-fractions are known explicitly, but in any case the coefficients $a_n$ can always be calculated from the power-series coefficients by means of the quotient-difference algorithm; see Table 3.10.1. …

44: 23.20 Mathematical Applications

… ►Given $P$, calculate $2P$, $4P$, $8P$ by doubling as above. …

45: 31.11 Expansions in Series of Hypergeometric Functions

… ►Series of Type II (§31.11(iv)) are expansions in orthogonal polynomials, which are useful in calculations of normalization integrals for Heun functions; see Erdélyi (1944) and §31.9(i). …

46: Bibliography D

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A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.

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Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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47: 1.3 Determinants, Linear Operators, and Spectral Expansions

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Formal Calculation of Determinants

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48: 3.2 Linear Algebra

… ►When $𝐀$ is a symmetric matrix, the left and right eigenvectors coincide, yielding $\kappa (\lambda )=1$, and the calculation of its eigenvalues is a well-conditioned problem. …

49: 19.21 Connection Formulas

… ►Because $R_G$ is completely symmetric, $x,y,z$ can be permuted on the right-hand side of (19.21.10) so that $(x-z)(y-z)\le 0$ if the variables are real, thereby avoiding cancellations when $R_G$ is calculated from $R_F$ and $R_D$ (see §19.36(i)). …

50: 1.13 Differential Equations

… ►As the interval $[a,b]$ is mapped, one-to-one, onto $[0,c]$ by the above definition of $t$, the integrand being positive, the inverse of this same transformation allows $\widehat{q}(t)$ to be calculated from $p,q,\rho$ in (1.13.31), $p,\rho \in C^2(a,b)$ and $q\in C(a,b)$. …