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Best approximations and interpolating functions


Author: John R. Rice
Journal: Trans. Amer. Math. Soc. 101 (1961), 477-498
MSC: Primary 41.40
DOI: https://doi.org/10.1090/S0002-9947-1961-0152790-3
MathSciNet review: 0152790
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  • [1] N. I. Achieser, Theory of approximation, New York, Frederick Ungar, 1956. MR 0095369 (20:1872)
  • [2] L. Fejér, Über die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Art entspringen, Math. Ann. vol. 85 (1922) pp. 41-48. MR 1512043
  • [3] D. Jackson, On functions of closest approximation, Trans. Amer. Math. Soc. vol. 22 (1921) pp. 117-128. MR 1501163
  • [4] -, Note on a class of polynomials of approximation, Trans. Amer. Math. Soc. vol. 22 (1921) pp. 320-326. MR 1501177
  • [5] T. S. Motzkin, Approximation by curves of a unisolvent family, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 789-793. MR 0031111 (11:101f)
  • [6] T. S. Motzkin and J. L. Walsh, Least pth power polynomials on a real finite point set, Trans. Amer. Math. Soc. vol. 78 (1955) pp. 67-81. MR 0066492 (16:585g)
  • [7] -, Least pth power polynomials on a finite point set, Trans. Amer. Math. Soc. vol. 83 (1956) pp. 371-396. MR 0081991 (18:479g)
  • [8] -, Polynomials of best approximation on a real finite point set. I, Trans. Amer. Math. Soc. vol. 91 (1959) pp. 231-245. MR 0108673 (21:7388)
  • [9] -, Polynomials of best approximation on an interval, Proc. Nat. Acad. Sci. U.S.A. vol. 45 (1959) pp. 1523-1528. MR 0119004 (22:9773)
  • [10] -, Best approximations within a linear family on an interval, Proc. Nat. Acad. Sci. U.S.A. vol. 46 (1960) pp. 1225-1233. MR 0162077 (28:5279)
  • [11] J. R. Rice, The characterization of best nonlinear Tchebycheff approximations, Trans. Amer. Math. Soc. vol. 96 (1960) pp. 322-340. MR 0117490 (22:8269)
  • [12] -, Tchebycheff approximation by functions unisolvent of variable degrees, Trans. Amer. Math. Soc. vol. 99 (1961) pp. 298-302. MR 0136913 (25:374)

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DOI: https://doi.org/10.1090/S0002-9947-1961-0152790-3
Article copyright: © Copyright 1961 American Mathematical Society

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