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The Fourier series operational matrix of integration. (English) Zbl 0558.44004
A general expression of the Fourier series operational matrix of integration P is derived. This matrix has most of its elements zero, a fact which makes this matrix computationally appealing. Furthermore, due to the integral properties of the sine and cosine functions, the approximation involved in $\int\sp{t}\sb{a}...\int\sp{t}\sb{a}\phi (\sigma)(d\sigma)\sp k\approx P\sp k\phi (t)$ could be better as compared to other orthogonal functions for example the Walsh functions. This matrix P may be used to solve problems like identification, analysis and optimal control.
Reviewer: S.P.Goyal

44A45Classical operational calculus
93E12System identification (stochastic systems)
93C15Control systems governed by ODE
33C45Orthogonal polynomials and functions of hypergeometric type
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
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