Clenshaw%E2%80%93Curtis

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1: Bibliography C

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A method for numerical integration on an automatic copmputer. Numer. Math. 2 (4), pp. 197–205.

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ISSN 0029-599X, Document, MathReview (A. H. Stroud), ZentralBlatt

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§3.5(iv).

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Generalized exponential and logarithmic functions. Comput. Math. Appl. Part B 12 (5-6), pp. 1091–1101.

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ISSN 0886-9561, MathReview (M. E. Muldoon), ZentralBlatt

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§4.12.

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Algorithms for special functions. I. Numer. Math. 4, pp. 403–419.

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ISSN 0029-599X, Document, MathReview (A. S. Householder), ZentralBlatt

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§5.24(ii).

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Level-Index Arithmetic: An Introductory Survey. In Numerical Analysis and Parallel Processing (Lancaster, 1987), P. R. Turner (Ed.), Lecture Notes in Math., Vol. 1397, pp. 95–168.

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MathReview Entry, ZentralBlatt

Referenced by:

§3.1(iv).

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Beyond floating point. J. Assoc. Comput. Mach. 31 (2), pp. 319–328.

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Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.1(iv).

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2: 3.5 Quadrature

… ►If we add $-1$ and $1$ to this set of $x_k$, then the resulting closed formula is the frequently-used Clenshaw–Curtis formula, whose weights are positive and given by … ►For further information, see Mason and Handscomb (2003, Chapter 8), Davis and Rabinowitz (1984, pp. 74–92), and Clenshaw and Curtis (1960). ►For detailed comparisons of the Clenshaw–Curtis formula with Gauss quadrature (§3.5(v)), see Trefethen (2008, 2011). … ► …

3: Bibliography P

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Modified Clenshaw-Curtis method for the computation of Bessel function integrals. BIT 23 (3), pp. 370–381.

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ISSN 0006-3835, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(vii).

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Stacking models of vesicles and compact clusters. J. Statist. Phys. 80 (3–4), pp. 755–779.

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Document, ZentralBlatt

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§8.24(ii).

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4: Bibliography T

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LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.

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Single-precision Fortran.

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ISSN 0010-4655, Document, Code

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9th item.

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Is Gauss quadrature better than Clenshaw-Curtis?. SIAM Rev. 50 (1), pp. 67–87.

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ISSN 0036-1445, Document, MathReview (Kai Diethelm), ZentralBlatt

Referenced by:

§3.5(iv).

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5: Bibliography O

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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

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Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

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Bounds for the solutions of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.

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MathReview (C. W. Clenshaw), ZentralBlatt

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§2.9(i).

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Numerical evaluation of the dilogarithm of complex argument. Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.

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ISSN 0923-2958, Document, MathReview (Bruce C. Berndt), ZentralBlatt

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§25.18(i).

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6: 4.47 Approximations

… ►Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for $\ln$, $\exp$, $\sin$, $\cos$, $\tan$, $\cot$, $\arcsin$, $\arctan$, $\mathrm{arcsinh}$. …

7: Bibliography W

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Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT 46 (1), pp. 195–202.

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ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(iv).

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Rational Chebyshev approximations for the Bessel functions $J_0(x)$, $J_1(x)$, $Y_0(x)$, $Y_1(x)$ . Math. Comp. 39 (160), pp. 617–623.

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Notes:

Tables on microfiche

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ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt

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9th item.

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8: 5.24 Software

… ►See also Borwein and Zucker (1992), Carmignani and Tortorici Macaluso (1985), Clenshaw et al. (1962), Cody (1991), Filho and Schwachheim (1967), and Temme (1994a). …

9: 29.20 Methods of Computation

… ►The Fourier series may be summed using Clenshaw’s algorithm; see §3.11(ii). …

10: 4.12 Generalized Logarithms and Exponentials

… ►For further information, see Clenshaw et al. (1986). …