Formulation of Linear Programs in Analysis. I: Approximation Theory

Abstract

Previous article Next article Formulation of Linear Programs in Analysis. I: Approximation TheoryR. J. Duffin and L. A. KarlovitzR. J. Duffin and L. A. Karlovitzhttps://doi.org/10.1137/0116054PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. C. Buck, H. L. Garabedian, Applications of duality in approximation theory, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964), Elsevier Publ. Co., Amsterdam, 1965, 27–42 MR0196367 0147.11204 Google Scholar[2] V. N. Burov, Approximation of functions by polynomials satisfying non-linear relations, Dokl. Akad. Nauk SSSR, 138 (1961), 515–517 MR0132339 0122.30901 Google Scholar[3] E. W. Cheney and , A. A. Goldstein, Tchebycheff approximation and related extremal problems, J. Math. Mech., 14 (1965), 87–98 MR0173896 0158.15102 ISIGoogle Scholar[4] B. R. Kripke and , T. J. Rivlin, Approximation in the metric of $L\sp{1}(X,\,\mu )$, Trans. Amer. Math. Soc., 119 (1965), 101–122 MR0180848 0135.35101 ISIGoogle Scholar[5] R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc., 95 (1960), 238–255 MR0113125 0096.31102 Google Scholar[6] J. R. Rice, Approximation with convex constraints, J. Soc. Indust. Appl. Math., 11 (1963), 15–32 10.1137/0111002 MR0159170 0116.04501 LinkISIGoogle Scholar[7] T. J. Rivlin and , H. S. Shapiro, A unified approach to certain problems of approximation and minimization, J. Soc. Indust. Appl. Math., 9 (1961), 670–699 10.1137/0109056 MR0133636 0111.06103 LinkISIGoogle Scholar[8] Ivan Singer, Caractérisation des éléments de meilleure approximation dans un espace de Banach quelconque, Acta Sci. Math. Szeged, 17 (1956), 181–189 MR0084620 0072.13003 Google Scholar[9] S. I. Zuhovickii˘, On approximation of real functions in the sense of P. L. Čebyšev, Uspehi Mat. Nauk (N.S.), 11 (1956), 125–159 MR0085380 Google Scholar[10] Preston C. Hammer, Topologies of approximation, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 1 (1964), 69–75 MR0176434 0287.41021 LinkGoogle Scholar[11] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York, 1966ix+294 MR0193469 0141.30503 Google Scholar[12] A. N. Kolmogorov, A remark on the polynomials of P. L. Čebyšev deviating the least from a given function, Uspehi Matem. Nauk (N.S.), 3 (1948), 216–221 MR0025609 Google Scholar[13] Günter Meinardus, Approximation von Funktionen und ihre numerische Behandlung, Springer Tracts in Natural Philosophy, Vol. 4, Springer-Verlag, Berlin, 1964viii+180 MR0176272 0124.33103 CrossrefGoogle Scholar[14] R. C. Jones and , L. A. Karlovitz, Iterative construction of constrained Chebyshev approximation of continuous functions, SIAM J. Numer. Anal., 5 (1968), 574–585 10.1137/0705046 MR0234187 0263.65014 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Characterizing best isotone approximations in Lp spaces, 1≤p<∞Journal of Approximation Theory, Vol. 203 Cross Ref Considerations on weak linear spaces Cross Ref A Characterization of Completeness via Absolutely Convergent Series and the Weierstrass Test in Asymmetric Normed Semilinear SpacesAbstract and Applied Analysis, Vol. 2014 Cross Ref Completeness, precompactness and compactness in finite-dimensional asymmetrically normed latticesTopology and its Applications, Vol. 160, No. 15 Cross Ref 𝐿¹-approximation with constraints1 January 1990 | Transactions of the American Mathematical Society, Vol. 322, No. 1 Cross Ref Best approximation as a solution of a gameAdvances in Mathematics, Vol. 47, No. 3 Cross Ref Least-squares approximation with restricted rangeJournal of Approximation Theory, Vol. 36, No. 4 Cross Ref The norm of a linear functional with respect to a non-negative convex functional vanishing at the originJournal of Mathematical Analysis and Applications, Vol. 78, No. 2 Cross Ref The conditional constant as error variable in the evaluation of stability constants from combined pH and pM measurementsAnalytica Chimica Acta, Vol. 116, No. 1 Cross Ref Extension with larger norm and separation with double support in normed linear spaces17 April 2009 | Bulletin of the Australian Mathematical Society, Vol. 21, No. 1 Cross Ref Approximation with constraints in normed linear spacesJournal of Approximation Theory, Vol. 21, No. 3 Cross Ref Isotonic Optimization in Tariff Construction29 August 2014 | ASTIN Bulletin, Vol. 8, No. 2 Cross Ref Some Algorithms for Computing Best Approximations from Convex ConesFrank Deutsch, John H. McCabe, and George M. Phillips14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 12, No. 3AbstractPDF (1286 KB)Numerical treatment of a class of semi-infinite programming problemsNaval Research Logistics Quarterly, Vol. 20, No. 3 Cross Ref Approximation with Convex ConstraintsJames T. Lewis18 July 2006 | SIAM Review, Vol. 15, No. 1AbstractPDF (2399 KB)Asymptotic duality over closed convex setsJournal of Mathematical Analysis and Applications, Vol. 35, No. 3 Cross Ref Nichtlineare Tschebyscheff Approximation mit Nebenbedingungen: AnwendungenNumerische Mathematik, Vol. 14, No. 4 Cross Ref Duality Inequalities of Mathematics and Science Cross Ref Zur Theorie der nichtlinearen Tschebyscheff-Approximation mit NebenbedingungenNumerische Mathematik, Vol. 14, No. 1 Cross Ref Iterative Construction of Constrained Chebyshev Approximation of Continuous FunctionsR. C. Jones and L. A. Karlovitz14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 3AbstractPDF (987 KB) Volume 16, Issue 4| 1968SIAM Journal on Applied Mathematics History Submitted:24 May 1967Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116054Article page range:pp. 662-675ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics