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On a class of best nonlinear approximation problems


Author: Samuel Karlin
Journal: Bull. Amer. Math. Soc. 78 (1972), 43-49
MSC (1970): Primary 41A50, 41A30; Secondary 41A55, 30A82
DOI: https://doi.org/10.1090/S0002-9904-1972-12842-8
MathSciNet review: 0291695
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  • 1. P. J. Davis, Interpolation and approximation, Blaisdell, New York, 1963. MR 28 #393. MR 157156
  • 2. U. Eckhardt, Einige Eigenschaften Wilfscher Quadraturformeln, Numer. Math. 12 (1968), 1-7. MR 41 #1217. MR 256561
  • 3. S. Karlin, Best quadrature formulas and splines, Approximation Theory 4 (1971), 59-90. MR 276661
  • 4. S. Karlin, Total positivity. Vol. 1, Stanford Univ. Press, Stanford, Calif., 1968. MR 37 #5667. MR 230102
  • 5. S. Karlin, The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas, Proc. Sympos. Approximations with Special Emphasis on Spline Functions (Univ. of Wisconsin, Madison, Wis., 1969), Academic Press, New York, 1969, pp. 467-484. MR 41 #2276. MR 257626
  • 6. S. Karlin and C. Michelli, The fundamental theorem of algebra for monosplines satisfying certain boundary conditions, J. Analyse Math. (to appear).
  • 7. S. Karlin and L. Schumaker, The fundamental theorem of algebra for Tchebycheffian monosplines, J. Analyse Math. 20 (1967), 233-270. MR 36 #582. MR 217493
  • 8. S. Karlin and W. J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Appl. Math., vol. 15, Interscience, New York, 1966. MR 34 #4757. MR 204922
  • 9. N. Richter, Numerical interpolation and approximation in Hilbert spaces, Rep. Dep. Appl. Math., Weizmann Inst. Sci., Rehovot, Israel.
  • 10. J. Sacks and N. D. Ylvisaker, Designs for regression problems with correlated errors, Ann. Math. Statist. 37 (1966), 66-89. MR 33 #826. MR 192601
  • 11. J. Sacks and N. D. Ylvisaker, Designs for regression problems with correlated errors; Many parameters, Ann. Math. Statist. 39 (1968), 49-69. MR 36 #3484. MR 220424
  • 12. G. Wahba, On the regression design problem of Sacks and Ylvisaker, Ann. Math. Statist. 42 (1971), 1035-1053. MR 279955
  • 13. J. R. Rice, The approximation of functions. Vol. II: Nonlinear and multivariate theory, Addison-Wesley, Reading, Mass., 1969. MR 39 #5989. MR 244675

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DOI: https://doi.org/10.1090/S0002-9904-1972-12842-8

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