spectral methods

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11: Bibliography M

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Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

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Notes:

Includes Fortran code, maximum accuracy 20S.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

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Geometrical and Catastrophe Optics Methods in Scattering. In Physical Acoustics, A. D. Pierce and R. N. Thurston (Eds.), Vol. 21, pp. 1–234.

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§36.14(ii).

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Numerical Methods for Roots of Polynomials. Part I. Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.

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ISBN 978-0-444-52729-5; 0-444-52729-X, MathReview Entry, ZentralBlatt

Referenced by:

§3.8(iv).

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Spectral functions for the Tomonaga-Luttinger model. Phys. Rev. B 46 (24), pp. 15753–15760.

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Document

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§13.28(iii).

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Methods and Programs for Mathematical Functions. Ellis Horwood Ltd., Chichester.

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Notes:

Includes diskette

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ISBN 0-13-578998-2, MathReview, ZentralBlatt

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2nd item, CEPHES (free C library).

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12: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►A survey is given of the formal spectral theory of second order differential operators, typical results being presented in §1.18(i) through §1.18(viii). … ►One then needs a self-adjoint extension of a symmetric operator to carry out its spectral theory in a mathematically rigorous manner. … ►Spectral expansions of $T$, and of functions $F(T)$ of $T$, these being expansions of $T$ and $F(T)$ in terms of the eigenvalues and eigenfunctions summed over the spectrum, then follow: … ►

Spectral expansions and self-adjoint extensions

… ►The reader is referred to Coddington and Levinson (1955), Friedman (1990, Ch. 3), Titchmarsh (1962a), and Everitt (2005b, pp. 45–74) and Everitt (2005a, pp. 272–331), for detailed methods and results. …

13: Bibliography E

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Notes:

Links to software for elliptic curve methods of factorization and primality testing.

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Home Page

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4th item.

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Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.

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ISBN 3-540-60230-5, MathReview (Alfred Actor), ZentralBlatt

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§25.17.

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A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112 (1-2), pp. 55–69.

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ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(vii).

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The Sobolev orthogonality and spectral analysis of the Laguerre polynomials $\{L_n^{-k}\}$ for positive integers $k$ . J. Comput. Appl. Math. 171 (1-2), pp. 199–234.

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ISSN 0377-0427, Document, Link, MathReview (Khélifa Trimèche)

Referenced by:

§18.36(v).

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14: Bibliography R

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Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.

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ISBN 978-0-12-585002-5, MathReview Entry

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§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

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ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

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Methods of Modern Mathematical Physics, Vol. 3, Scattering Theory. Academic Press, New York.

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ISBN 0-12-585003-4 (vol.3), MathReview (P. R. Chernoff)

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§1.18(x).

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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15: Bibliography K

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Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J..

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Notes:

Includes collection of single- and double-precision Fortran subroutines.

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ISBN 0-13-627258-4, GAMS (package NMS), ZentralBlatt

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NMS (free collection of Fortran subroutines).

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Periodic Orbits, Spectral Statistics, and the Riemann Zeros. In Supersymmetry and Trace Formulae: Chaos and Disorder, J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner (Eds.), pp. 1–15.

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§25.17.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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The Rayleigh function: Theory and computational methods. Zh. Vychisl. Mat. Mat. Fiz. 39 (12), pp. 1962–2006.

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Translation in Comput. Math. Math. Phys. 39 (1999), No. 12, pp. 1883–1925.

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ISSN 0044-4669, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.21(xiii).

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An indirect method for evaluating certain infinite integrals. Z. Angew. Math. Phys. 29 (3), pp. 380–386.

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ISSN 0044-2275, Document, MathReview, ZentralBlatt

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§10.71(ii).

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16: 31.8 Solutions via Quadratures

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$ϵ=-m_3+\frac{1}{2}$ , $m_0,m_1,m_2,m_3=0,1,2,\mathrm{\dots }$,

►the Hermite–Darboux method (see Whittaker and Watson (1927, pp. 570–572)) can be applied to construct solutions of (31.2.1) expressed in quadratures, as follows. … ►The variables $\lambda$ and $\nu$ are two coordinates of the associated hyperelliptic (spectral) curve $\mathrm{\Gamma }:{\nu }^2={\prod }_{j=1}^{2g+1}(\lambda -{\lambda }_j)$. …

17: Bibliography O

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Asymptotic Enumeration Methods. In Handbook of Combinatorics, Vol. 2, L. Lovász, R. L. Graham, and M. Grötschel (Eds.), pp. 1063–1229.

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ISBN 0-444-82351-4, Pdf, MathReview (Konrad Engel), ZentralBlatt

Referenced by:

Ch.2.

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Computing $\pi (x)$: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.

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Notes:

Online fulltext contains postpublication annotations.

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FullText

Referenced by:

§27.18.

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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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A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.

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Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(ii).

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Spectral decomposition of tent maps using symmetry considerations. J. Statist. Phys. 84 (1-2), pp. 269–276.

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ISSN 0022-4715, Document, MathReview (Makoto Mori), ZentralBlatt

Referenced by:

§24.18.

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18: Bibliography L

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Computing $\pi (x)$: The Meissel-Lehmer method. Math. Comp. 44 (170), pp. 537–560.

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ISSN 0025-5718, FullText, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§27.18.

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An efficient derivative-free method for solving nonlinear equations. ACM Trans. Math. Software 11 (3), pp. 250–262.

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Notes:

Corrigendum, ibid. 15(3) (1989), 287

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ISSN 0098-3500, Document, MathReview (T. Feagin), ZentralBlatt

Referenced by:

§3.8(iii).

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Introduction to spectral theory: selfadjoint ordinary differential operators. Translations of Mathematical Monographs, Vol. 39, American Mathematical Society, Providence, R.I..

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Notes:

Translated from the Russian by Amiel Feinstein

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MathReview Entry

Referenced by:

§1.18(x).

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The spectral analysis of three families of exceptional Laguerre polynomials. J. Approx. Theory 202, pp. 5–41.

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ISSN 0021-9045, Document, Link, MathReview (Edmundo J. Huertas)

Referenced by:

§18.36(vi).

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Linear prediction of bandlimited processes with flat spectral densities. IEEE Trans. Signal Process. 49 (7), pp. 1564–1569.

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ISSN 1053-587X, Document, MathReview, ZentralBlatt

Referenced by:

§30.15(v).

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19: Bibliography B

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COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method. Comput. Phys. Comm. 27, pp. 147–166.

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Notes:

Double-precision Fortran code for positive energies. Maximum accuracy: 31S.

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Document, Code

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2nd item, 2nd item.

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Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.

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Document, MathReview (Bernard Harris), ZentralBlatt

Referenced by:

Ch.2.

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A new asymptotic representation for $\zeta (\frac{1}{2}+it)$ and quantum spectral determinants. Proc. Roy. Soc. London Ser. A 437, pp. 151–173.

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ISSN 0962-8444, MathReview (Jack Quine), ZentralBlatt

Referenced by:

§25.9.

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. Methods Appl. Anal. 2 (4), pp. 475–489.

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ISSN 1073-2772, Pdf, MathReview (Dan Polis̆evski), ZentralBlatt

Referenced by:

§2.4(iv).

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20: Bibliography P

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Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.

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ISSN 1364-5021, Document, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§10.20(ii).

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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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A survey of numerical methods for the computation of Bessel function integrals. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 249–265.

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Notes:

International conference on special functions: theory and computation (Turin, 1984)

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ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations. J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.

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External Links:

Document

Referenced by:

§10.76(ii).

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A method for computing Bessel function integrals. J. Comput. Phys. 75 (2), pp. 334–344.

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ISSN 0021-9991, Document, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§10.74(vii), §10.74(vii).

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