Convergence rates of methods with smooth initial error

Authors:
Robert E. Lynch and John R. Rice

Journal:
Math. Comp. **22** (1968), 311-335

MSC:
Primary 65.65

DOI:
https://doi.org/10.1090/S0025-5718-1968-0237109-1

MathSciNet review:
0237109

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References | Similar Articles | Additional Information

**[1]**N. I. Achieser,*Theory of approximation*, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956. MR**0095369****[2]**Garrett Birkhoff, Richard S. Varga, and David Young,*Alternating direction implicit methods*, Advances in Computers, Vol. 3, Academic Press, New York, 1962, pp. 189–273. MR**0168131****[3]**C. de Boor & J. R. Rice, "Chebyshev approximation by and application to ADI iteration,"*J. Soc. Indust. Appl. Math.*, v. 11, 1963, pp. 159-169. MR**28**#4666.**[4]**Willis H. Guilinger Jr.,*The Peaceman-Rachford method for small mesh increments*, J. Math. Anal. Appl.**11**(1965), 261–277. MR**0183125**, https://doi.org/10.1016/0022-247X(65)90086-7**[5]**R. E. Lynch, J. R. Rice, and D. H. Thomas,*Tensor product analysis of partial difference equations*, Bull. Amer. Math. Soc.**70**(1964), 378–384. MR**0169390**, https://doi.org/10.1090/S0002-9904-1964-11105-8**[6]**Robert E. Lynch, John R. Rice, and Donald H. Thomas,*Direct solution of partial difference equations by tensor product methods*, Numer. Math.**6**(1964), 185–199. MR**0213047**, https://doi.org/10.1007/BF01386067**[7]**Robert E. Lynch, John R. Rice, and Donald H. Thomas,*Tensor product analysis of alternating direction implicit methods*, J. Soc. Indust. Appl. Math.**13**(1965), 995–1006. MR**0198699****[8]**D. W. Peaceman and H. H. Rachford Jr.,*The numerical solution of parabolic and elliptic differential equations*, J. Soc. Indust. Appl. Math.**3**(1955), 28–41. MR**0071874****[9]**J. R. Rice,*The Approximation of Functions*, Vol. II, Addison-Wesley, Reading, Mass. (To appear.)**[10]**Dunham Jackson,*The theory of approximation*, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR**1451140****[11]**Antoni Zygmund,*Trigonometrical series*, Dover Publications, New York, 1955. MR**0072976****[12]**Carl de Boor,*Bicubic spline interpolation*, J. Math. and Phys.**41**(1962), 212–218. MR**0158512**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0237109-1

Article copyright:
© Copyright 1968
American Mathematical Society