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Topic: Numerical analysis


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  Numerical analysis - Wikipedia, the free encyclopedia
Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics).
The field of numerical analysis is divided in different disciplines according to the problem that is to be solved.
Numerical analysis is also concerned with computing (in an approximate way) the solution of differential equations, both ordinary differential equations and partial differential equations.
en.wikipedia.org /wiki/Numerical_analysis   (1751 words)

  
 Numerical analysis Info - Encyclopedia WikiWhat.com
Numerical analysis is that branch of applied mathematics which studies the methods and algorithms to find (approximate) numerical solutions to various mathematical problems, using a finite sequence of arithmetic and logical operations.
Accuracy - the numerical approximation should be as accurate as possible and the error should be possible to estimate according to some scale.
Numerical Analysis is also concerned with computing (in an approximate way) the solution of Partial Differential Equations.
www.wikiwhat.com /encyclopedia/n/nu/numerical_analysis_1.html   (662 words)

  
 The Math Forum - Math Library - Numerical Analysis   (Site not responding. Last check: 2007-10-22)
Numerical Analysis preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives.
Numerical solutions to differential equations require the determination not of a few numbers but of an entire function; in particular, convergence must be judged by some global criterion.
BIT emphasizes numerical methods in approximation, linear algebra, and ordinary and partial differential equations, but also publishes papers in areas such as numerical functional analysis and numerical optimization.
mathforum.org /library/topics/num_analysis   (2195 words)

  
 Numerical Analysis of Applied Partial Differential Equations
Numerical analysis is the mathematical method that uses numerical approximations to obtain numerical answers to the problem.
Numerical analysis also considers the accuracy of an approximation, and when the approximation is good enough.
Numerical methods are needed most in situations with variable coefficients, inhomogeneities, or time dependent boundary conditions.
www.geocities.com /b_ward.rm/na.html   (1809 words)

  
 Numerical Analysis at Portsmouth   (Site not responding. Last check: 2007-10-22)
Integral equations --> Numerical Analysis is the area of Mathematics and Computer Science concerned with the solution of Mathematical problems using a Computer.
Numerical Analysis has applications in all areas of Science and Technology.
Numerical Analysis sector at the Dept. of Mathematics, Univ. of Portsmouth
www.tech.port.ac.uk /staffweb/makrogla/numerical_analysis.html   (661 words)

  
 Numerical Analysis
The ability of a numerical method to control the effect of approximation errors is often one of the most crucial factors in determining which method to use.
The problems involved with such an innocuous task are useful to motivate the study of numerical analysis.
In the next numerical analysis lectures we will consider the problems involved in more advanced numerical methods, such as the solution of ordinary and partial differential equations, finding eigenvalues, and optimization methods (such as genetic algorithms).
www.hpcc.ecs.soton.ac.uk /training/numan_i.html   (1833 words)

  
 Numerical Analysis Group Publications   (Site not responding. Last check: 2007-10-22)
J.F. Blowey and H. Garcke, Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility, SIAM Journal of Numerical Analysis 37, 286-318.
Straughan, Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions, J. Math.
J.F. Blowey, M.I.M. Copetti and C.M. Elliott, The numerical analysis of a model for phase separation of a multi-component alloy, IMA Journal of Numerical Analysis, 16 111-139.
fourier.dur.ac.uk:8000 /num/num_reps.html   (1382 words)

  
 Numerical Analysis Technical Reports
Numerical methods for both ordinary differential equations (ODEs) and delay differential equations (DDEs) are traditionally developed and assessed on the basis of how well the accuracy of the approximate solution is related to the specified error tolerance on an adaptively-chosen, discrete mesh.
This may not be appropriate in numerical investigations that require visualization of an approximate solution on a continuous interval of interest (rather than at a small set of discrete points) or in investigations that require the determination of the `average' values or the `extreme' values of some solution components.
Numerical results demonstrate that the QSC methods are optimal, that is, fourth order locally at certain points and third order globally, even for some problems that do not satisfy the conditions of the analysis.
www.cs.toronto.edu /NA/reports.html   (14589 words)

  
 numerical analysis --¬† Encyclop√¶dia Britannica
Because of the complexity of the analysis—many characters are measured on many individuals or a number of species—the use of a computer is virtually mandatory.
The following is a rough categorization of the mathematical theory underlying numerical analysis, keeping in mind that there is often a great deal of overlap between the listed areas.
Chemical analysis answers these and many other questions by providing a way to determine the nature of any substance in terms of the elements...
www.britannica.com /eb/article-9108506   (784 words)

  
 Numerical Analysis and Scientific Computing
Research ranges from basic numerical analysis (finite element, boundary element and finite difference convergence theory) and fast methods (multigrid) to applications in materials science (foam evolution, phase transformations in crystalline alloys, approximation of microstructure, visco-elastic phenomena) and electromagnetism (scattering, inverse scattering and ferromagentism).
Numerical analysis and scientific computing presentations are often featured in the Applied Mathematics seminar series.
Students wishing to study numerical analysis or scientific computing usually enroll in the Applied Mathematics graduate program (see The Graduate Program web pages for more details).
www.math.udel.edu /research/na/NA.html   (324 words)

  
 UofT DCS Numerical Analysis Research Group Info
The area of numerical analysis is often called numerical computation, numerical methods, numerical mathematics, computational mathematics, scientific computing or mathematical software, depending which aspect of this broad subject that is being emphasized.
One can argue that the reason computers were invented was to perform numerical computations, and scientific computing continues to be one of the main driving forces in the development of advanced computing architectures.
Although we emphasize the numerical solution of differential equations, we are also active in several other areas, including special functions, polynomial root finders, linear algebra, optimization and language facilities for numerical computation.
www.cs.toronto.edu /DCS/Research/numerical.html   (339 words)

  
 Numerical Analysis at the University of Kansas
His interest is in the analysis and computation of spectra for nonautonomous linear homogeneous differential equations, analysis and computation of lattice differential equations, in particular traveling wave solutions, and in bringing together our study of spectra as a tool for the existence and stability of traveling waves.
This research has as a central theme the combination of dynamical systems and numerical analysis ideas, and our interests are in the development and analysis of efficient, accurate numerical techniques that are useful for the computation and analysis of dynamical systems.
His goal is to develop the numerical methods that make use of matrix structures and that produce numerical solutions with the required structures, so that the numerical results are computed accurately and quickly, and are meaningful to the underlying application.
www.math.ku.edu /~evanvleck/napage/napage.html   (1223 words)

  
 Numerical Analysis
A point that is probably a surprise for many numerical analysts (and it was a surprise for me, too) is that not just formal integrability but indeed involution is of importance here.
I show that obstructions to involution may turn into integrability conditions upon semi-discretisation so that even if the original system is formally integrable but not involutive, the DAE obtained by the semi-discretisation has hidden integrability conditions.
In I have studied the numerical properties of the Hamilton-Dirac equations, the equations of motion derived with the Dirac bracket.
www.iwr.uni-heidelberg.de /groups/compalg/seiler/Research/numana.html   (556 words)

  
 Texas A&M Numerical Methods for PDE Group   (Site not responding. Last check: 2007-10-22)
The numerical methods group is primarily concerned with the efficient numerical approximation of solutions of partial differential equations.
The techniques and expertise include the development and analysis of iterative methods, stability and error analysis for finite element, finite difference and finite volume approximations, and large scale scientific computation with industrial application.
As well as doing research into theoretical numerical analysis, the group works closely with the Institute for Scientific Computation in the development of large scale scientific simulations for serial and parallel computing architectures.
www.math.tamu.edu /research/numerical_analysis   (129 words)

  
 Numerical Analysis -index.html
For this edition, we have added a large number of new exercises, and numerous notes that detail some of the history of numerical analysis.
Many of us teaching numerical analysis in the past few years have found that students are increasingly using a computer algebra system to perform the required calculations.
The link Numerical Analysis Programs provides the programs in the various formats and instructions for their implementation.
www.as.ysu.edu /~faires/Numerical-Analysis   (840 words)

  
 SAL- Numerical Analysis - Miscellaneous Software
Schelab -- a numerical analysis library for Scheme.
Template Numerical Toolkit (TNT) -- a numeric library for scientific computing in C++ (mainly linear algebra routines).
Numerical Integration -- collection of FORTRAN code for numerical computation of integrals.
sal.jyu.fi /B/0/index.shtml   (1605 words)

  
 Amazon.com: Numerical Analysis : Mathematics of Scientific Computing: Books: David R. Kincaid,E. Ward Cheney   (Site not responding. Last check: 2007-10-22)
This highly successful and scholarly book introduces students with diverse backgrounds to the various types of mathematical analysis that are commonly needed in scientific computing.
The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with careful proofs and scientific background.
The underlying structure of numerical analysis never developed and I was left swimming in meaningless details while the basics were short-changed by an over abundance of specialized algorithms.
www.amazon.com /exec/obidos/tg/detail/-/0534389058?v=glance   (635 words)

  
 Numerical Analysis Books using DERIVE from Chartwell-Yorke
This book covers the major numerical methods, and their analysis, for first courses at college and undergraduate level.
Each chapter includes the development and algebraic analysis of the methods, lab-based activities, ideas for coursework, case studies, exercises and solutions.
Chapter 1 introduces the basic tool of numerical methods, which is recurrence relations, their solution and ill-conditioning problems.
www.chartwellyorke.com /numanbks.html   (215 words)

  
 NA Resources
Outline of Numerical Analysis Topics: This set of webpages provide information about numerical analysis topics that students are expected to learn in numerical analysis course.
With minimal expertise and a powerful computer, the novice may now boldly attempt to simulate the physical world in which we are all embedded.
Numerical Methods that Works, Forman Acton, reprinted by MAA, 1990, originally published in 1970.
www.math.byu.edu /~schow/resources   (795 words)

  
 Open Directory - Science: Math: Numerical Analysis
Holistic Numerical Methods Institute - A collection of resources on numerical methods aimed at undergraduates, maintained at the University of South Florida.
Numerical Analysis Resources FAQ - Maintained by Steve Sullivan.
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.
dmoz.org /Science/Math/Numerical_Analysis   (408 words)

  
 65: Numerical analysis
Numerical analysis involves the study of methods of computing numerical data.
This includes computational issues in group theory, number theory, geometry, statistics, and so on; for each of these fields there are software packages or libraries of code which are discussed on those index pages.
Applications of numerical analysis occur throughout the fields of applied (numerical) mathematics, in particular in the fields of physics (sections 70-86).
www.math.niu.edu /~rusin/known-math/index/65-XX.html   (1442 words)

  
 The Univ. of Iowa, Numerical Analysis Group
He is also interested in numerical integration, multivariable polynomial interpolation and approximation theory, and the numerical solution of the radiosity equation from computer graphics.
Numerical Objects AS develops and markets technical and scientific software for the university, governmental and commercial markets, world-wide.
Visual Numerics, producers of general purpose numerical analysis software, including the IMSL library.
www.math.uiowa.edu /faculty/researchGroups/numanal.htm   (476 words)

  
 Numerical Analysis 22C:170/22M:170
The Definition of Numerical Analysis as discussed by L. Trefethen.
An Overview of Numerical Analysis by Kendall Atkinson.
Discuss the numerical method used in light of the output you produce.
www.math.uiowa.edu /~atkinson/m170.html   (576 words)

  
 Amazon.com: Numerical Analysis: Books: Richard L. Burden,J. Douglas Faires   (Site not responding. Last check: 2007-10-22)
Schaum's Outline of Numerical Analysis by Francis Scheid
If you are already knowledgeable on the subject of numerical analysis this book might be a good reference for refreshing your memory but for the beginner it is for the most part going to be a frustrating waste of time.
I took a numerical analysis course last semester at my university and had a horrible time understanding this book.
www.amazon.com /exec/obidos/tg/detail/-/0534955320?v=glance   (1492 words)

  
 Group 18, MATH 317 - Numerical Analysis   (Site not responding. Last check: 2007-10-22)
The first part was to develop and describe the process of making an algorithm of the Newton-Raphson method to numerically solve a system of n equations of n variables.
The second part was to form a code to solve a system with 3 equations, 3 variables, given a decent initial guess.
Below are the parts of the project in their appropriate categories.
www.math.mcgill.ca /nigam/NA/groups/group18   (285 words)

  
 Numerical Algorithms Group
NAG announces major new release of its numerical library for C and C++ programmers
NAG's mathematical and statistical components underpin thousands of programs and applications spanning the globe in industries as diverse as financial analysis, science and engineering, and in academia and research.
Whether you are using a single PC or a cluster of the world's largest supercomputers, NAG has the numerical software capabilities to suit your model.
www.nag.co.uk   (293 words)

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