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Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). Some of the problems it deals with arise directly from the study of calculus; other areas of interest are real variable or complex variable questions, numerical linear algebra over the real or complex fields, the solution of differential equations, and other related problems arising in the physical sciences and engineering.
General introduction
Many problems in continuous mathematics do not possess a closed-form solution. Examples are finding the integral of exp(−x2) (see error function) and solving a general polynomial equation of degree five or higher (see Abel-Ruffini theorem). In these situations, one has two options left: either one tries to find an approximate solution using asymptotic analysis or one seeks a numerical solution. The latter choice describes the field of numerical analysis.
More on [ Numerical analysis ]
Pseudorandom Numbers :: Algorithms
In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions
tjdemas (T.J. Demas) Wed, 04 Nov 2009 00:42:19 -0000
In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions
Success of modern science is application of continuous mathematics. But this isn't adequate to explain all features of universe.
strtweets (Stand to Reason) Wed, 28 Oct 2009 02:55:03 -0000
Success of modern science is application of continuous mathematics. But this isn't adequate to explain all features of universe.
Domain Decomposition Organization - Bergen, Norway. Information about the annual international Domain Decomposition meeting, links to people working in the field and information about books and other material related to Domain Decomposition.
External Numerical Analysis Sources - Compiled by Nick Gould, Rutherford Appleton Laboratory.
Foundations of Computational Mathematics (FoCM) - A nonprofit organization that supports and promotes research on foundations of computational mathematics.
Holistic Numerical Methods Institute - A collection of resources on numerical methods aimed at undergraduates, maintained at the University of South Florida.
Interval Computations - Indexes links relating to interval arithmetic and related issues.
Inverse Symbolic Calculator - Programs and specialized tables of mathematical constants dedicated to the identification of real numbers: a project at the Centre for Experimental and Constructive Mathematics.
IPNet - Inverse Problems Network, for the area of inverse or ill-posed problems.
Level Set and Fast Marching Methods: - Tracking moving interfaces in computational geometry, materials sciences, robotics, image processing, and fluid mechanics; numerical techniques based on partial differential equations.
Meta Description: [ Web Page for Level Set Methods:
J.A. Sethian:
Fast Marching Methods and Level Set Methods are numerical techniques which can
follow the evolution of interfaces. These interfaces can develop sharp corners,
break apart, and merge together.
The techniques have a wide range of applications, incl... ]
MGNet - Multigrid method resources. Sites, publications, software.
N-Body/Particle Simulation Methods - Overview of N-body methods.
NA-Net - Searchable weekly email digest on numerical analysis.
Newton's Method and High-order Iterations - Newton's iteration : History, convergence results, Halley's iteration and high order new iterations. A web text in HTML and PostScript.
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Numerical Analysis Resources FAQ - Maintained by Steve Sullivan.
Meta Description: [
Mathcom Solutions provides software solutions
for finance, engineering, and operations.
Mathcom provides portfolio analysis software,
portfolio optimization software,
financial analysis, financial software,
financial engineering software,
engineering software,
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Numerical Methods - A guide to on-line resources.
Numerical Methods for PDEs with Java Applets - Distance learning course dealing with finite differences / elements, Monte-Carlo, Fourier and Lagrangian methods for the advection, diffusion, wave, Schrodinger, Burger and KdV equations. The commercial version of a course taught to science and engineering students at the Royal Institute of Technology in Stockholm (Sweden).
Meta Description: [ Interactive course showing how to use finite differences, finite elements, Fourier and Monte Carlo methods, using java applets to solve the advection, diffusion, Black-Scholes, KdV, Burger and the Schroedinger equations ]
On-line Numerical Methods - A web-based numerical methods simulator for student use.
Orthogonal Polynomials and Special Functions - SIAM activity group. Newsletter, conferences, bibliography, reports, history, jobs, other resources.
Search sci.math.num-analysis - Teachers and students of numerical analysis will find others who share their interests at the sci.math.num-analysis discussion list. Searchable archive at the Math Forum.
Solve Equations by Successive Approximations - Approximation formulae to compute real and complex solutions of equations in a spreadsheet.
SQRT - Algorithms for Calculating the Square Root - Describing two major algorithms: one efficient in terms of size, the other in terms of speed. English/Portuguese.
Meta Description: [ SQRT by Pedro Freire ]
Tomasz Plewa's Numerical Analysis Directory - Directory of sites containing software for numerical analysis (mainly in Fortran).
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