next up previous
Next: About this document Up: No Title Previous: Integration Errors

References

1
E. Bannai, R. M. Damerell. Tight spherical designs I. Journal Mathematical Society Japan, 31:199-207, 1979.

2
E. Bannai, R. M. Damerell. Tight spherical designs II. Journal London Mathematical Society, 21(2):13-30, 1980.

3
L. Bos. Some remarks on the Fejér-problem for Lagrange interpolation in several variables. Journal Approximation Theory, 60:133-140, 1990.

4
Richard H. Byrd, Peihuang Lu, Jorge Nocedal and Ciyou Zhu. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16(5), 1995. Also published as Technical Report NAM-08, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois, USA. May 1994. Electronically distributed as ftp://eecs.nwu.edu/pub/lbfgs/lbfgs_bcm/byrd-lu-nocedal-zhu.ps

5
Richard H. Byrd, Jorge Nocedal and Robert B. Schnabel. Representations of quasi-Newton matrices and their use in limited memory methods. Technical Report NAM-03, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois, USA. January 21, 1996. Electronically distributed as ftp://eecs.nwu.edu/pub/lbfgs/lbfgs_bcm/byrd-nocedal-schnabel.ps

6
R. Cools. The construction of cubature formulae using invariant theory and ideal theory. Ph. thesis, Leuven 1989.

7
J. Cui and W. Freeden. Equidistribution on the sphere. Bericht der Arbeitsgruppe Geomathematik, Nr. 142, Universität Kaiserslautern, 1995.

8
P. Delsarte, J. M. Goethals and J. J. Seidel. Sperical codes and designs. Geometriae Dedicata, 6:363-388, 1977.

9
Murray Dow. CONMIN code. Electronically distributed via ftp://anusf.anu.edu.au/mld900/constr_minimum

10
William L. Goffe, Gary D. Ferrier and John Rogers. Global optimization of statistical functions with simulated annealing. Journal of Econometrics, 60:65-99, 1994.

11
William L. Goffe, Gary D. Ferrier and John Rogers. SIMANN code. Electronically distributed as ftp://netlib2.cs.utk.edu/opt/simann.f

12
Lester Ingber. ASA Version 10.9. Code and accompanying documentation. Electronically distributed via http://www.ingber.com/#ASA-CODE and ftp://ftp.ingber.com

13
V. I. Krylov. Approximate calculation of integrals. ACM Monograph Series, Macmillan New York, London, 1962.

14
J. R. Morris, D. M. Deaven and K. M. Ho. Genetic-algorithm energy minimization for point charges on a sphere. Physical Review B, 53(4):1740-1743, 1996.

15
Stephen G. Nash. Newton-type minimization via the Lanczos method. SIAM Journal on Numerical Analysis, 21(4):770-778, 1984.

16
M. Reimer. Constructive theory of multivariate functions. BI Wissenschaftsverlag, Mannheim, Wien, Zürich 1990.

17
M. Reimer. On the existence-problem of Gauss-quadrature on the sphere. In: B.Fuglede e.a., eds., Approximation by solutions of partial differential equations, Kluwer 1992, 169-184.

18
M. Reimer. On the existence of Gauss-like node-distributions on high-dimensional spheres. In: K. Jetter and F. Utreras, eds., Multivariate Approximation, World Scientific 1993, 281-291.

19
M. Reimer. Quadrature rules for the surface integral of the unit sphere on extremal fundamental systems. Mathematische Nachrichten, 169:235-241, 1994.

20
M. Reimer, B. Sündermann. A Remez-type algorithm for the calculation of extremal fundamental systems for polynomial spaces on the sphere. Computing 37:43-58, 1986.

21
J. J. Seidel. Harmonics and Combinatorics. In: R. A. Askey. Special functions: Group theoretical aspects and applications, 287-303, D.Reidel Publishing Company 1984.

22
P. D. Seymour, T. Zaslavsky. Averaging sets: A generalization of mean values and spherical designs. Advances Mathematics, 52:231-240, 1984.

23
J. Steinacker, E. Thamm and U. Maier. Efficient integration of intensity functions on the sphere. Journal of Quantitative Spectroscopy and Radiative Transfer, 56(1):97-107, 1996.

24
A. H. Stroud, D. Secrest: Gaussian quadrature formulas. Prentice Hall Inc., Series in Automatic Computation, 1966.

25
Yanmu Zhou. Arrangements of points on the sphere. Ph. thesis, Tampa, Florida, 1995.

26
Ciyou Zhu. L-BFGS FORTRAN code. November 1994. Electronically distributed via ftp://eecs.nwu.edu/pub/lbfgs/lbfgs_bcm/ and http://www.eecs.nwu.edu/~ciyou/code/lbcode.html

27
Ciyou Zhu, Richard H. Byrd, Peihuang Lu and Jorge Nocedal. L-BFGS-B: a limited memory FORTRAN code for solving bound constrained optimization problems. Technical Report, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois, USA. 1994. Electronically distributed as ftp://eecs.nwu.edu/pub/lbfgs/lbfgs_bcm/zhu-byrd-lu-nocedal.ps

28
Ciyou Zhu, Richard H. Byrd, Peihuang Lu and Jorge Nocedal. L-BFGS-B -- FORTRAN subroutines for large-scale bound constrained optimization. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois, USA. December 31, 1994. Electronically distributed as ftp://eecs.nwu.edu/pub/ciyou/pp9.ps or via ftp://eecs.nwu.edu/pub/lbfgs/lbfgs_bcm/ and http://www.eecs.nwu.edu/~ciyou/index.html

next up previous
Next: About this document Up: No Title Previous: Integration Errors

Joerg Fliege
Thu Dec 23 19:39:35 CET 1999