Frank Stenger, University of Utah, email: stenger@sinc.utah.edu Guest

Posted: Fri Nov 29, 2002 3:32 pm Subject: New text related to wavelets




New text related to wavelets
I wish to announce the publication of my text, "Numerical Methods Based on
Sinc and Analytic Functions", by SpringerVerlag (ISBN 0387940081).
This text uses analytic function methods to derive the symbolic formulae
based on sinc functions, their approximation properties and error, and the
derivation of numerical algorithms based on these symbolic formulae for
solving a large class of problems stemming from applications. For example,
the DFT formula, which yields the wellknown FFT procedure is one of the
formulas of the class, but there are many others, such as new methods of
interpolation, quadrature, the approximation of derivatives, the
approximation of one and multidimensional indefinite or definite convolution
integrals, the approximate solution of ordinary differential equations, and
the approximation of Hilbert transforms, over arbitrary intervals or contours.
Included also are new methods of solving elliptic, parabolic, and hyperbolic
partial differential equations, new methods of solving linear and nonlinear
Volterra, Fredholm, multidimensional, and Cauchy singular integral equations,
and new methods of evaluating and inverting Laplace and Fourier transforms.
For example, the complexity, i.e., the amount of work required to obtain an
approximate solution of a partial differential equation in d dimensions to
within a tolerance of E is usually of the order of {log(E)}**(2d+2).
The methods excel for problems with endpoint singularities, for problems
over semiinfinite or infinite regions, or for boundary layer problems. 
