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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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
MathSciNet review: 0291695
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  • 2. Ulrich Eckhardt, Einige Eigenschaften Wilfscher Quadraturformeln, Numer. Math. 12 (1968), 1–7 (German). MR 0256561 (41 #1217)
  • 3. Samuel Karlin, Best quadrature formulas and splines, J. Approximation Theory 4 (1971), 59–90. MR 0276661 (43 #2403)
  • 4. Samuel Karlin, Total positivity. Vol. I, Stanford University Press, Stanford, Calif, 1968. MR 0230102 (37 #5667)
  • 5. Samuel Karlin, The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas, Approximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969) Academic Press, New York, 1969, pp. 467–484. MR 0257626 (41 #2276)
  • 6. S. Karlin and C. Michelli, The fundamental theorem of algebra for monosplines satisfying certain boundary conditions, J. Analyse Math. (to appear).
  • 7. Samuel Karlin and Larry Schumaker, The fundamental theorem of algebra for Tchebycheffian monosplines, J. Analyse Math. 20 (1967), 233–270. MR 0217493 (36 #582)
  • 8. 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, 1966. MR 0204922 (34 #4757)
  • 9. N. Richter, Numerical interpolation and approximation in Hilbert spaces, Rep. Dep. Appl. Math., Weizmann Inst. Sci., Rehovot, Israel.
  • 10. Jerome Sacks and N. Donald Ylvisaker, Designs for regression problems with correlated errors, Ann. Math. Statist. 37 (1966), 66–89. MR 0192601 (33 #826)
  • 11. Jerome Sacks and Donald Ylvisaker, Designs for regression problems with correlated errors; many parameters, Ann. Math. Statist. 39 (1968), 49–69. MR 0220424 (36 #3484)
  • 12. Grace Wahba, On the regression design problem of Sacks and Ylvisaker, Ann. Math. Statist. 42 (1971), 1035–1053. MR 0279955 (43 #5676)
  • 13. John R. Rice, The approximation of functions. Vol. 2: Nonlinear and multivariate theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0244675 (39 #5989)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1972-12842-8
PII: S 0002-9904(1972)12842-8