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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 \(\int^{t}_{a}...\int^{t}_{a}\phi (\sigma)(d\sigma)^ k\approx P^ k\phi (t)\) 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

MSC:

44A45 Classical operational calculus
93E12 Identification in stochastic control theory
93C15 Control/observation systems governed by ordinary differential equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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References:

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