Gaussian Numerical Fft

Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided.

Much of this book is concerned with autoregressive and moving av­ erage linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case.

Sante FFT Imaging is a program that removes pattern noise from DICOM and plain images (jpg, tif, png and bmp). This type of noise is very common in images that have been digitized with a CR digitizer. The program uses the Fast Fourier Transform (FFT), convolution low-pass filters in frequency domain or/and direct frequency deleting to eliminate the pattern noise.

A Practical Approach to Understand the Numerical Methods

This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay.

This text, covering a very large span of numerical methods and optimization, is primarily aimed at advanced undergraduate and graduate students. A background in calculus and linear algebra are the only mathematical requirements.