Titlebook: Wavelets Theory and Its Applications; A First Course Mani Mehra Textbook 2018 Springer Nature Singapore Pte Ltd. 2018 Fourier analysis.Mult

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Applications of Wavelet in Inverse Problemsject or a medium, from the observation of response of this object to a probing signal. Moreover, inverse problem is to deduce cause from an effect. There are always input and output parameters related to any physical system. If all the parameters were known perfectly, then for a given input, we can

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Textbook 2018mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The

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Wavelet-Galerkin Methodsoth spectral (discussed in Sect.?.) and finite difference (or finite element) bases (discussed in Sects.?. and .). In ., the degrees of freedom are the expansion coefficients of a set of basis functions and these expansion coefficients are not in physical space anymore (i.e., expansion coefficients are in wavelet space).

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Wavelet-Galerkin Methodsoth spectral (discussed in Sect.?.) and finite difference (or finite element) bases (discussed in Sects.?. and .). In ., the degrees of freedom are the expansion coefficients of a set of basis functions and these expansion coefficients are not in physical space anymore (i.e., expansion coefficients are in wavelet space).

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Other Wavelet-Based Numerical Methodsin Sect.?.), the differential operators [., .], or both [.]. .: Methods discussed in Sect.?. fall in this category. .: There are a few approaches that use wavelets in such a way that does not fit into anyone of previous categories and will be discussed in this chapter.

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Applications of Wavelet in Inverse Problemsere are always input and output parameters related to any physical system. If all the parameters were known perfectly, then for a given input, we can predict the output very easily, and this is called . (like advection–diffusion equation and Burgers’ equation discussed in Chap.?.).