Strong Unicity Research Articles

On the behavior of the strong unicity constant for changing dimension

On the behavior of the strong unicity constant for changing dimension

A counterexample to strong unicity in monotone approximation

A counterexample to strong unicity in monotone approximation

Unicity and strong unicity in approximation theory

Unicity and strong unicity in approximation theory

On an unboundedness conjecture for strong unicity constants

On an unboundedness conjecture for strong unicity constants

General properties of the Yang-Mills equations in physical space

With the formulation of the gauge group as a Banach-Lie group of suitable Sobolev type, the Cauchy problem for the Yang-Mills equation in physical space-time reduces rigorously to the case of the temporal gauge. In this gauge there exist spatially global strong solutions for given data for field and potential that are L(2) together with one or two derivatives (respectively). Regarding global existence in time, there is strong unicity, strong existence unless the potential becomes unbounded, and existence of a quasi-solution for arbitrary finite-energy Cauchy data. The variety of solutions of the equations is endowed with a canonical symplectic structure. This structure is degenerate to an extent precisely reflecting gauge-invariance and is conformally invariant.

Lipschitz and strong unicity constants for changing dimension

;I Tf,}& with lim,,m /! f -h 11 = 0 that lim,+, A(h) = h(f). For fixed f and n, Henry and Roulier [5] investigate the behavior of X(f) for changing intervals.

Eine Klasse von Verfahren zur Ermittlung bester nichtlinearer Tschebyscheff-Approximationen

Methods for constructing best nonlinear Chebyshev approximations are discussed. It is shown that local strong unicity is sufficient to guarantee "good numerical behaviour" of the algorithms. Applications are given for approximations by splines with free knots, rational functions, and exponential sums as well as for the approximation of functions defined by differential equations.

On Lipschitz conditions, strong unicity and a Theorem of A. K. Cline

On Lipschitz conditions, strong unicity and a Theorem of A. K. Cline

Characterizations of strong unicity in approximation theory

Characterizations of strong unicity in approximation theory

Uniform Generalized Weight Function Polynomial Approximation with Interpolation

Previous article Next article Uniform Generalized Weight Function Polynomial Approximation with InterpolationH. L. Loeb, D. G. Moursund, L. L. Schumaker, and G. D. TaylorH. L. Loeb, D. G. Moursund, L. L. Schumaker, and G. D. Taylorhttps://doi.org/10.1137/0706026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. Paszkowski, On approximation with nodes, Rozprawy Mat., 14 (1957), 63– MR0092888 0083.29002 Google Scholar[2] Frank Deutsch, On uniform approximation with interpolatory constraints, J. Math. Anal. Appl., 24 (1968), 62–79 10.1016/0022-247X(68)90049-8 MR0230017 0174.35501 CrossrefISIGoogle Scholar[3] E. W. Cheney and , H. L. Loeb, Generalized rational approximation, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 1 (1964), 11–25 MR0178288 0138.04403 LinkGoogle Scholar[4] Samuel Karlin and , William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966xviii+586 MR0204922 0153.38902 Google Scholar[5] David G. Moursund, Chebyshev approximation using a generalized weight function, SIAM J. Numer. Anal., 3 (1966), 435–450 10.1137/0703038 MR0204936 0163.07302 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A general framework for the optimal approximation of circular arcs by parametric polynomial curvesJournal of Computational and Applied Mathematics, Vol. 345 | 1 Jan 2019 Cross Ref Strong unicity of order 2 in C(T)Journal of Approximation Theory, Vol. 56, No. 3 | 1 Mar 1989 Cross Ref The Best Interpolating Approximation is a Limit of Best Weighted ApproximationsCanadian Mathematical Bulletin, Vol. 25, No. 4 | 20 November 2018 Cross Ref The best interpolating approximation and weighted approximationJournal of Approximation Theory, Vol. 35, No. 1 | 1 Oct 1982 Cross Ref Remez algorithm for Chebyshev approximation with interpolationComputing, Vol. 28, No. 1 | 1 Mar 1982 Cross Ref Discrete chebyshev approximation with interpolationInternational Journal of Computer Mathematics, Vol. 11, No. 3-4 | 19 March 2007 Cross Ref Approximation with interpolatory constraintsJournal of Mathematical Analysis and Applications, Vol. 64, No. 2 | 1 Jun 1978 Cross Ref Approximation with constraints in normed linear spacesJournal of Approximation Theory, Vol. 21, No. 3 | 1 Nov 1977 Cross Ref An alternation theory for copositive approximationJournal of Approximation Theory, Vol. 19, No. 2 | 1 Feb 1977 Cross Ref The Remez exchange algorithm for approximation with linear restrictionsTransactions of the American Mathematical Society, Vol. 223, No. 0 | 1 January 1976 Cross Ref Best uniform approximation with Hermite-Birkhoff interpolatory side conditionsJournal of Approximation Theory, Vol. 15, No. 2 | 1 Oct 1975 Cross Ref Optimal rational starting approximationsJournal of Approximation Theory, Vol. 12, No. 2 | 1 Oct 1974 Cross Ref Optimal starting approximations for iterative schemesJournal of Approximation Theory, Vol. 9, No. 1 | 1 Sep 1973 Cross Ref Approximation with Convex ConstraintsJames T. LewisSIAM Review, Vol. 15, No. 1 | 18 July 2006AbstractPDF (2399 KB)A generalization of the varisolvency and unisolvency propertiesJournal of Approximation Theory, Vol. 7, No. 1 | 1 Jan 1973 Cross Ref Nonlinear Tchebycheff approximation with constraintsJournal of Approximation Theory, Vol. 6, No. 3 | 1 Oct 1972 Cross Ref A unified approach to uniform real approximation by polynomials with linear restrictionsTransactions of the American Mathematical Society, Vol. 166, No. 0 | 1 January 1972 Cross Ref Kolmogoroff's criterion for constrained rational approximationJournal of Approximation Theory, Vol. 4, No. 2 | 1 Jun 1971 Cross Ref Uniform rational approximation with osculatory interpolationJournal of Computer and System Sciences, Vol. 4, No. 6 | 1 Dec 1970 Cross Ref Approximation by functions having restricted ranges: Equality caseNumerische Mathematik, Vol. 14, No. 1 | 1 Dec 1969 Cross Ref Volume 6, Issue 2| 1969SIAM Journal on Numerical Analysis161-315 History Submitted:30 September 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706026Article page range:pp. 284-293ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

Uniform Approximation by Chebyshev Spline Functions. II: Free Knots

Abstract : Existence, uniqueness and characterization of best uniform approximations of continuous functions by (Tchebycheffian) spline functions with free knots in (a,b) are investigated. (Author)

Applications of the Hahn-Banach Theorem in Approximation Theory

Applications of the Hahn-Banach Theorem in Approximation Theory

On $L_1 $ Approximation II: Computation for Discrete Functions and Discretization Effects

On $L_1 $ Approximation II: Computation for Discrete Functions and Discretization Effects