×
Cheney, E. W.; Goldstein, A. A.

Newton’s method for convex programming and Tschebyscheff approximation. (English) Zbl 0113.10703

Numer. Math. 1, 253-268 (1959).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0113.10703

Cited in 117 Documents

Keywords:

numerical analysis
PDF BibTeX XML Cite
\textit{E. W. Cheney} and \textit{A. A. Goldstein}, Numer. Math. 1, 253--268 (1959; Zbl 0113.10703)
Full Text: DOI EuDML

References:

[1] Remez, E.: Sur un, Procédé Convergent d’Approximations Successives pour Determiner les Polynomes d’Appproximation. C. R. Acad. Sci. Paris198, 2063-2065 (1934). · JFM 60.0211.03
[2] Remez, E.: Sur le Calcul Effectif des Polynomes d’Approximation deTschebyscheff. C. R. Acad. Sci. Paris199, 337-340 (1934). · JFM 60.0212.01
[3] Remez, E. Ya.: On the Method of Best, in the Sense ofTchebycheff, Approximate Representation of Functions, (Ukrainian), Kiev, 1935. See also Reference 4 below.
[4] Remez, E. Ya. General Computation Methods for Chebyshev Approximation. Problems with Real Parameters Entering Linearly. Izdat. Akad. Nauk Ukrainsk. SSR. Kiev, 1957. 454 pp. See also MR 19-580 (Russian).
[5] Novodvorskii, E. N., andI. Sh. Pinsker: On a Process of Equalization of Maxima, Uspehi Matem. Nauk, N. S.6, 174-181 (1951). See alsoShenitzer, A.: Chebyshev Approximations. J. Assoc. Comput. Mach.4, 30-35 (1957). MR 13-728.
[6] Beale, E. M. L.: An Alternative Method for Linear Programming. Proc. Cambridge Philos. Soc.50, 512-523 (1954). MR 16-155. · Zbl 0056.13705
[7] Beale, E. M. L.: On Minimizing, a Convex Function Subject to Linear Inequalities. J. Roy. Stat. Soc., Ser. B17, 173-177 (1955). · Zbl 0068.13701
[8] Bratton, Donald: New Results in the Theory and Techniques of Chebyshev Fitting. Abstract 546-34. Notices Am. Math. Soc.5, 248 (1958).
[9] Stiefel, Eduard L.: Numerical Methods of Tchebycheff Approximation, pp. 217-232 inR. E. Langer (ed.), On Numerical Approximation. Madison 1959. 480 pp. · Zbl 0083.35502
[10] Stiefel, E.: Über diskrete und lineare Tschebyscheff-Approximationen. Numerische Mathematik1, 1-28 (1959). · Zbl 0083.11501
[11] Wolfe, Philip: Programming with Nonlinear Constraints. Preliminary Report, Abstract 548-102. Notices Am. Math. Soc.5, 508 (1958).
[12] Stone, Jeremy J. The Cross Section Method, presented orally at Symposium for Mathematical Programming, RAND Corporation, March 19, 1959.
[13] Kelley, James E.: A General Technique for Convex Programming, presented orally at Symposium on Mathematical Programming, RAND Corporation, March 19, 1959.
[14] Cheney, E. W., andA. A. Goldstein: Proximity Maps for Convex Sets. Proc. Amer. Math. Soc.10, 448-450 (1959). · Zbl 0092.11403
[15] Bonnesen, T., u.W. Fenchel: Theorie der konvexen Körper. Berlin 1934. · Zbl 0008.07708
[16] Fan, K.: On Systems of Linear Inequalities. In: Linear Inequalities and Related Systems, ed., byH. W. Kuhn andA. W. Tucker, pp. 99-156. Princeton 1956. · Zbl 0072.37602
[17] Bram, Joseph: Chebychev Approximation in Locally Compact Spaces. Proc. Am. Math. Soc.9, 133-136 (1958). · Zbl 0080.04402
[18] Goldstein, A. A., andE. W. Cheney: A Finite Algorithm for the Solution of Consistent Linear Equations and Inequalities and for the Tchebycheff Approximation of Inconsistent Linear Equations. Pac. J. Math.8, 415-427 (1958). · Zbl 0084.01902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.