Paper
3 September 2008 The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients
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Abstract
In this paper, we establish the optimum interpolation approximation for a set of multi-dimensional statistical orthogonal expansions. Each signal has a bounded linear combination of higher order self-correlations and mutual-correlations with respect to coefficients of the expansion. For this set of signals, we present the optimum interpolation approximation that minimizes various worst-case measures of mean-square error among all the linear and the nonlinear approximations. Finally, as a practical application of the optimum interpolation approximation, we present a discrete numerical solution of linear partial differential equations with two independent variables.
© (2008) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Yuichi Kida and Takuro Kida "The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients", Proc. SPIE 7075, Mathematics of Data/Image Pattern Recognition, Compression, and Encryption with Applications XI, 70750E (3 September 2008); https://doi.org/10.1117/12.795760
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Cited by 1 scholarly publication.
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KEYWORDS
Numerical analysis

Partial differential equations

Error analysis

Stochastic processes

Nonlinear optics

Fourier transforms

Multidimensional signal processing

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