Best approximations and interpolating functions
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- by John R. Rice PDF
- Trans. Amer. Math. Soc. 101 (1961), 477-498 Request permission
References
- N. I. Achieser, Theory of approximation, Frederick Ungar Publishing Co., New York, 1956. Translated by Charles J. Hyman. MR 0095369
- Leopold Fejér, Über die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Art entspringen, Math. Ann. 85 (1922), no. 1, 41–48 (German). MR 1512043, DOI 10.1007/BF01449600
- Dunham Jackson, On functions of closest approximation, Trans. Amer. Math. Soc. 22 (1921), no. 1, 117–128. MR 1501163, DOI 10.1090/S0002-9947-1921-1501163-1
- Dunham Jackson, Note on a class of polynomials of approximation, Trans. Amer. Math. Soc. 22 (1921), no. 3, 320–326. MR 1501177, DOI 10.1090/S0002-9947-1921-1501177-1
- Th. Motzkin, Approximation by curves of a unisolvent family, Bull. Amer. Math. Soc. 55 (1949), 789–793. MR 31111, DOI 10.1090/S0002-9904-1949-09286-8
- T. S. Motzkin and J. L. Walsh, Least $p$th power polynomials on a real finite point set, Trans. Amer. Math. Soc. 78 (1955), 67–81. MR 66492, DOI 10.1090/S0002-9947-1955-0066492-2
- T. S. Motzkin and J. L. Walsh, Least $p$th power polynomials on a finite point set, Trans. Amer. Math. Soc. 83 (1956), 371–396. MR 81991, DOI 10.1090/S0002-9947-1956-0081991-6
- T. S. Motzkin and J. L. Walsh, Polynomials of best approximation on a real finite point set. I, Trans. Amer. Math. Soc. 91 (1959), 231–245. MR 108673, DOI 10.1090/S0002-9947-1959-0108673-9
- J. L. Walsh and T. S. Motzkin, Polynomials of best approximation on an interval, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1523–1528. MR 119004, DOI 10.1073/pnas.45.10.1523
- J. L. Walsh and T. S. Motzkin, Best approximators within a linear family on an interval, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 1225–1233. MR 162077, DOI 10.1073/pnas.46.9.1225
- John R. Rice, The characterization of best nonlinear Tchebycheff approximations, Trans. Amer. Math. Soc. 96 (1960), 322–340. MR 117490, DOI 10.1090/S0002-9947-1960-0117490-3
- John R. Rice, Tchebycheff approximations by functions unisolvent of variable degree, Trans. Amer. Math. Soc. 99 (1961), 298–302. MR 136913, DOI 10.1090/S0002-9947-1961-0136913-8
Additional Information
- © Copyright 1961 American Mathematical Society
- 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