Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Complex Chebyshev polynomials on circular sectors with degree six or less
HTML articles powered by AMS MathViewer

by U. Grothkopf and G. Opfer PDF
Math. Comp. 39 (1982), 599-615 Request permission


Let $T_n^\alpha$ denote the nth Chebyshev polynomial on the circular sector ${S^\alpha } = \{ z:|z| \leqslant 1,|\arg z| \leqslant \alpha \}$. This paper contains numerical values of ${\left \| {T_n^\alpha } \right \|_\infty }$ and the corresponding coefficients of $T_n^\alpha$ for $n = 1(1)6$ and $\alpha = {0^ \circ }({5^ \circ }){180^ \circ }$. Also all critical angles for $T_n^\alpha ,n = 1(1)6$ are listed, where an angle is called critical when the number of absolute maxima of $|T_n^\alpha |$ changes at that angle. All figures are given to six places. The positions (and hence the number) of extremal points of $T_n^\alpha ,n = 1(1)6$ are presented graphically. The method consists of a combination of semi-infinite linear programming, finite linear programming, and Newton’s method.
    M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, fifth printing, Dover, New York, 1968. J. P. Coleman & A. J. Monaghan, Chebyshev Expansions for the Bessel Function ${J_n}(z)$ in the Complex Plane, University of Durham, 1980. (Preprint.) G. H. Elliott, Polynomial Approximation in the Complex Plane Using Generalised Humbert Polynomials, Lecture at Dundee Biennial Conference on Numerical Analysis, 1981.
  • Carl Geiger and Gerhard Opfer, Complex Chebyshev polynomials on circular sectors, J. Approx. Theory 24 (1978), no. 2, 93–118. MR 511466, DOI 10.1016/0021-9045(78)90001-1
  • K. Glashoff & S. Å. Gustafson, Einführung in die lineare Optimierung, Wissenschaftliche Buchgesellschaft, Darmstadt, 1978.
  • K. Glashoff and K. Roleff, A new method for Chebyshev approximation of complex-valued functions, Math. Comp. 36 (1981), no. 153, 233–239. MR 595055, DOI 10.1090/S0025-5718-1981-0595055-4
  • R. Hettich, Numerical methods for nonlinear Chebyshev approximation, Approximation in Theorie und Praxis (Proc. Sympos., Siegen, 1979) Bibliographisches Inst., Mannheim, 1979, pp. 139–156. MR 567658
  • Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482
  • Gerhard Opfer, An algorithm for the construction of best approximations based on Kolmogorov’s criterion, J. Approx. Theory 23 (1978), no. 4, 299–317 (English, with German summary). MR 509560, DOI 10.1016/0021-9045(78)90082-5
  • R. L. Streit & A. H. Nuttall, Linear Chebyshev Complex Function Approximation, Technical Report 6403, Naval Underwater Systems Center, Newport, R. I., New London, Conn., 1981.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 30E10, 65D20
  • Retrieve articles in all journals with MSC: 30E10, 65D20
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 599-615
  • MSC: Primary 30E10; Secondary 65D20
  • DOI:
  • MathSciNet review: 669652