In this paper an overview of wavelet based multiresolution analyses is presented. First, the
continuous wavelet transform in its simplest form is discussed. Then, the definition of a …

The solution of a partial differential equation can be obtained by computing the inverse
operator map between the input and the solution space. Towards this end, we introduce a …

In the nearly seven years since I finished writing the first edition of this book research on the
accuracy and stability of numerical algorithms has continued to flourish and mature. Our …

We present the lifting scheme, a simple construction of second generation wavelets; these
are wavelets that are not necessarily translates and dilates of one fixed function. Such …

A group of algorithms is presented generalizing the fast Fourier transform to the case of
noninteger frequencies and nonequispaced nodes on the interval -π,π. The schemes of this …

A new version of the Fast Multipole Method for the Laplace equation in three dimensions Page
1 ActaNumerica (1997), pp. 229-269 © Cambridge University Press, 1997 A new version of the …

Most existing books on wavelets are either too mathematical or they focus on too narrow a
specialty. This book provides a thorough treatment of the subject from an engineering point …

Efficient numerical solution of realistic and, therefore, complex equation systems occupies
many researchers in many disciplines. For various reasons, but mainly in order to …

A class of multiwavelet bases for L^2 is constructed with the property that a variety of integral
operators is represented in these bases as sparse matrices, to high precision. In particular …

The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …