On alternation numbers in nonlinear Chebyshev approximation. (English) Zbl 0395.41013
Keywords:
Nonlinear Chebyshev Approximation; Alternation Numbers; Uniqueness of the Chebyshev Operator; Continuous Dependence of Best Approximation; Positive Exponential Sums; Locally Best Approximation; Globally Best Approximations; Gamma Polynomials; Continuity of the Chebyshev OperatorReferences:
| [1] | Arndt, H., On uniqueness of best spline approximations with free knots, J. Approximation Theory, 11, 118-125 (1974) · Zbl 0283.41004 |
| [2] | Barrar, R. B.; Loeb, H. L., On the continuity of the nonlinear Tschebyscheff operator, Pacific J. Math., 32, 593-601 (1970) · Zbl 0192.42003 |
| [3] | de Boor, C., On the approximation by γ-polynomials, (Schoenberg, I. J., Approximations with Special Emphasis on Spline Functions (1969), Academic Press: Academic Press New York/London) · Zbl 0273.41014 |
| [4] | Braess, D., Über die Vorzeichenstruktur der Exponentialsummen, J. Approximation Theory, 3, 101-113 (1970) · Zbl 0191.35802 |
| [5] | Braess, D., Chebyshev approximation by spline functions with free knots, Numer. Math., 17, 357-366 (1971) · Zbl 0227.65010 |
| [6] | Braess, D., Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation, Math. Z., 132, 327-341 (1973) · Zbl 0251.41010 |
| [7] | Braess, D., Chebyshev approximation by γ-polynomials, I, J. Approximation Theory, 9, 20-43 (1973) · Zbl 0235.41007 |
| [8] | Braess, D., Chebyshev approximation by γ-polynomials, II, J. Approximation Theory, 11, 16-37 (1974) · Zbl 0235.41008 |
| [9] | Braess, D., On the number of best approximations in certain nonlinear families of functions, Aequationes Math., 12, 184-199 (1975) · Zbl 0304.41014 |
| [10] | Cheney, E. W., Introduction to Approximation Theory (1966), McGraw-Hill: McGraw-Hill New York · Zbl 0161.25202 |
| [11] | Dubovickii, A. J.; Miljutin, A. A., Extremum problems in the presence of restrictions, USSR Comput. Math. Math. Phys., 5, 1-80 (1965) · Zbl 0158.33504 |
| [12] | Dunham, O., Partly alternating families, J. Approximation Theory, 6, 378-386 (1972) · Zbl 0246.41024 |
| [13] | Meinardus, G.; Schwedt, D., Nichtlineare Approximation, Arch. Rat. Mech. Anal., 17, 297-326 (1964) · Zbl 0127.29001 |
| [14] | Rice, J. R., Tschebyscheff approximations by functions unisolvent of variable degree, Trans. Amer. Math. Soc., 99, 298-302 (1961) · Zbl 0146.08301 |
| [15] | Rice, J. R., (The Approximation of Functions, Vol. II (1969), Addison-Wesley: Addison-Wesley Reading, Mass) · Zbl 0185.30601 |
| [16] | Schmidt, E., Zur Kompaktheit bei Exponentialsummen, J. Approximation Theory, 3, 445-454 (1970) · Zbl 0212.09103 |
| [17] | Schmidt, E., Stetigkeitsaussagen bei der Tschebyscheff-Approximation mit positiven Exponentialsummen, J. Approximation Theory, 4, 13-20 (1971) · Zbl 0212.09201 |
| [18] | Schumaker, L. L., Uniform approximation by Tchebycheffian spline functions, J. Math. Mech., 18, 369-378 (1968) · Zbl 0165.38603 |
| [19] | Schumaker, L. L., Uniform approximation by Chebyshev spline functions. II. Free knots, SIAM J. Numer. Anal., 5, 647-656 (1968) · Zbl 0169.39404 |
| [20] | Werner, H., Vorlesung über Approximationstheorie, (Lecture Notes in Mathematics, Vol. 14 (1966), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0135.26705 |
| [21] | Werner, H., Der Existenzsatz für das Tschebyscheffsche Approximationsproblem mit Exponentialsummen, (International Series of Numerical Mathematics (1967), Birkhäuser-Verlag: Birkhäuser-Verlag Basel/Stuttgart) · Zbl 0189.35201 |
| [22] | Werner, H.; Schaback, R., (Praktische Mathematik, Vol. II (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0259.65001 |
| [23] | Wulbert, D., Uniqueness and differential characterization of approximations from manifolds of functions, Amer. J. Math., 93, 350-366 (1971) · Zbl 0227.41009 |
| [24] | Wulbert, D., Nonlinear approximation with tangential characterization, Amer. J. Math., 93, 718-730 (1971) · Zbl 0227.41010 |
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