Numerical Analysis

NUMERICAL ANALYSIS

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The Division of Numerical Analysis

This topic page is for organising the development of Numerical analysis content on Wikiversity.

If you are knowledgeable in any area Numerical analysis, feel free to improve, we would greatly appreciate your contributions.

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of continuous mathematics (as distinguished from discrete mathematics).

As a topic of study, it has a large overlap with Numerical Algorithms and Scientific Computing.

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Learning projects and learning resources

Since there is already a lot of material on this topic freely available, we will try to organize and supplement, rather than duplicate. In particular, here we collect exercises and quizzes, which would be inappropriate for Wikipedia. The topics are organized and ordered as in Wikipedia's w:List of numerical analysis topics. A topic is only listed here if we have something to add, such as a Wikibook link (prefaced with b:), a learning module here, further examples, exercises, quizzes, or links to external learning resources.

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Topics

Causes of Errors w: Loss of Significance, Loss of Significance Numerical Linear Algebra w:Matrix norm, exercises w:LU decomposition, exercises, concept quiz w:Power iteration, exercises, examples w:Inverse iteration, exercises shifted inverse iteration w:Householder transformation, exercises Topic:Numerical Analysis/Matrix norm Iterative Refinement

Interpolation w: Polynomial interpolation Using the Vandermonde matrix, example, exercise w: Lagrange polynomial, example, exercise w: Newton polynomial w: Divided differences, proofs and examples Polynomial example, exercise w: Neville's algorithm, examples, quiz, code Interpolation_and_Extrapolation Comparison of the methods, concept quiz Cubic Spline Interpolation

Finding roots of nonlinear equations Rootfinding for nonlinear equations The bisection method Exercises on the bisection method Solution of the exercises on the bisection method The Newton's method Resources about rootfinding for nonlinear equations The Secant Method w: Fixed-point iteration, Fixed Point Iteration

Optimization

Integration and Differentiation Differentiation, examples Error of Analysis of Newton-Cotes formulas w: Romberg's method, Romberg's Integration method, Sample Code, Example, Exercise, Quiz w: Gaussian Quadrature, Gaussian Quadrature

Ordinary Differential Equations w: Truncation error (numerical integration), Truncation Errors w:Euler_method w:Runge-Kutta stability of RK methods exercises quiz Order of RK methods w:Multistep_methods Adams-bashforth and Adams-moulton methods stability of Multistep methods ODE Exercises ODE in vector form Exercises Quiz

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Other Resources

• Boundary Value Problems/Numerical Methods
• Introduction to Numerical Methods and Matlab Programming, a free online text for a college junior level course Applied Numerical Methods.
• NumaWWW, offers the possibility of testing a lot of methods from numerical computing and optimization interactively, with only minimal programming knowledge needed.
• MA213: Numerical Analysis is a free online course.
• Holistic Numerical Methods collects undergraduate resources and learning materials.