Linear filtering

Author:
Ralph Shapiro

Journal:
Math. Comp. **29** (1975), 1094-1097

MSC:
Primary 93E10

DOI:
https://doi.org/10.1090/S0025-5718-1975-0389356-X

MathSciNet review:
0389356

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Abstract: A simple linear smoothing operator of general order *p* is constructed for discretized functions. It is particularly suited for problems in numerical integration where it is necessary or desirable to suppress two-grid-interval waves. The operator is ideal in the sense that for the class of damping operators of order *p*, which remove two-grid-interval waves without changing the phase of any wave component, this operator produces the least damping of the amplitudes of all other waves.

**[1]**B. G. HUNT, "Zonally symmetric global general circulation models with and without the hydrologic cycle,"*Tellus*, v. 25, 1973, pp. 337-354.**[2]**B. G. HUNT, "A global general circulation model of the atmosphere based on the semispectral method,"*Monthly Weather Review*, v. 102, 1974, pp. 3-16.**[3]**R. SHAPIRO, "Smoothing, filtering, and boundary effects,"*Rev. Geophys. and Space Phys.*, v. 8, 1970, pp. 359-387.**[4]**R. SHAPIRO, "The use of linear filtering as a parameterization of atmospheric diffusion,"*J. Atmospheric Sci.*, v. 28, 1971, pp. 523-531.

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DOI:
https://doi.org/10.1090/S0025-5718-1975-0389356-X

Article copyright:
© Copyright 1975
American Mathematical Society