Numerical analysis is the study of algorithms for the problems of continuous mathematics, those that involve real or complex variables and typically use numerical approximation in addition to symbolic manipulation. Rather than giving exact symbolic answers, it seeks approximate solutions within specified error bounds. It finds application in engineering and the physical sciences and, more recently, in the life and social sciences, with examples that include ordinary differential equations in celestial mechanics, numerical linear algebra in data analysis, and the simulation of living cells. Before modern computers, numerical methods relied on hand interpolation from large printed tables such as the Abramowitz and Stegun handbook; since the mid twentieth century computers calculate the required functions instead. Its key concerns include direct and iterative methods, conditioning, discretization, and the generation and propagation of round-off and truncation errors.
Facts
Core ConcernAlgorithms for the problems of continuous mathematics 1 Connections
Includes
Source Adjoint state method (Wikipedia)
Source Alternating-direction implicit method (Wikipedia)
Source Boole's rule (Wikipedia)
Source Borwein's algorithm (Wikipedia)
Source Discontinuous Galerkin method (Wikipedia)
Source Douglas Hartree (Wikipedia)
Source Finite-difference time-domain method (Wikipedia)
Source Gertrude Blanch (Wikipedia)
Source Inverse quadratic interpolation (Wikipedia)
Source ITP method (Wikipedia)
Source Leslie Comrie (Wikipedia)
Source Liu Hui's π algorithm (Wikipedia)
Source Method of lines (Wikipedia)
Source Nested sampling algorithm (Wikipedia)
Source Peter Borwein (Wikipedia)
Source Proper generalized decomposition (Wikipedia)
Source Rayleigh-Ritz method (Wikipedia)
Source Relaxation (iterative method) (Wikipedia)
Source Trapezoidal rule (differential equations) (Wikipedia)
Source Volume of fluid method (Wikipedia)
In the Other Atlases
Same As
Also in Mathematics Atlas: the same subject.
Sources
1. Cornell ABC Book: Numerical Analysis
Numerical Analysis entry, definition attributed to Nick Trefethen
is the study of algorithms for problems of continuous mathematics
Numerical Analysis entry, opening definition
is the study of algorithms for problems of continuous mathematics
View the SourceWikipedia: Numerical analysis
WikipediaIn Group: Computing for the Sciences and Engineering, Lead, applicationsQuote, In Group: Computing for the Sciences and Engineering, Lead, applications
Numerical analysis finds application in all fields of engineering and the physical sciences
Liu Hui's π algorithm (Wikipedia)
Includes: Liu Hui's π algorithm, LeadQuote, Includes: Liu Hui's π algorithm, Lead
Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of π to any accuracy.
Inverse quadratic interpolation (Wikipedia)
Includes: Inverse quadratic interpolation, Lead, fieldQuote, Includes: Inverse quadratic interpolation, Lead, field
In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form f(x) = 0.
Rayleigh-Ritz method (Wikipedia)
Includes: Rayleigh-Ritz method, For matrix eigenvalue problems, fieldQuote, Includes: Rayleigh-Ritz method, For matrix eigenvalue problems, field
In numerical linear algebra, the Rayleigh-Ritz method is commonly applied to approximate an eigenvalue problem
Boole's rule (Wikipedia)
Includes: Boole's rule, Lead, fieldQuote, Includes: Boole's rule, Lead, field
numerical quadrature
Method of lines (Wikipedia)
Includes: Method of lines, Lead, fieldQuote, Includes: Method of lines, Lead, field
the numerical integration of ordinary differential equations
Finite-difference time-domain method (Wikipedia)
Includes: Finite-difference time-domain method, LeadQuote, Includes: Finite-difference time-domain method, Lead
is a numerical analysis technique used for modeling computational electrodynamics
Trapezoidal rule (differential equations) (Wikipedia)
Includes: Trapezoidal rule (differential equations), Lead, fieldQuote, Includes: Trapezoidal rule (differential equations), Lead, field
In numerical analysis and scientific computing, the trapezoidal rule is a numerical method
Discontinuous Galerkin method (Wikipedia)
Includes: Discontinuous Galerkin method, Lead, fieldQuote, Includes: Discontinuous Galerkin method, Lead, field
form a class of numerical methods for solving differential equations
Borwein's algorithm (Wikipedia)
Includes: Borwein's algorithm, Lead, numerical computationQuote, Includes: Borwein's algorithm, Lead, numerical computation
Each additional term of the partial sum yields approximately 25 digits.
Peter Borwein (Wikipedia)
Includes: Peter Borwein, ResearchQuote, Includes: Peter Borwein, Research
to produce a very rapidly convergent series suitable for high precision numerical calculations
Nested sampling algorithm (Wikipedia)
Includes: Nested sampling algorithm, Background, fieldQuote, Includes: Nested sampling algorithm, Background, field
it is necessary to employ a numerical algorithm to find an approximation
Leslie Comrie (Wikipedia)
Includes: Leslie Comrie, CareerQuote, Includes: Leslie Comrie, Career
where he also pioneered the teaching of numerical analysis
Douglas Hartree (Wikipedia)
Includes: Douglas Hartree, CareerQuote, Includes: Douglas Hartree, Career
most famous for the development of numerical analysis
Gertrude Blanch (Wikipedia)
Includes: Gertrude Blanch, CareerQuote, Includes: Gertrude Blanch, Career
did pioneering work in numerical analysis and computation
Adjoint state method (Wikipedia)
Includes: Adjoint state method, Lead, numerical methodQuote, Includes: Adjoint state method, Lead, numerical method
The adjoint state method is a numerical method for efficiently computing the gradient
Volume of fluid method (Wikipedia)
Includes: Volume of fluid method, LeadQuote, Includes: Volume of fluid method, Lead
numerical techniques for tracking and locating the free surface
ITP method (Wikipedia)
Includes: ITP method, Lead, fieldQuote, Includes: ITP method, Lead, field
In numerical analysis, the ITP method (Interpolate Truncate and Project method) is the first root-finding algorithm
Alternating-direction implicit method (Wikipedia)
Includes: Alternating-direction implicit method, Lead, first sentenceQuote, Includes: Alternating-direction implicit method, Lead, first sentence
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.
Relaxation (iterative method) (Wikipedia)
Includes: Relaxation (iterative method), Lead, first sentenceQuote, Includes: Relaxation (iterative method), Lead, first sentence
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.
Proper generalized decomposition (Wikipedia)
Includes: Proper generalized decomposition, Lead, numerical methodQuote, Includes: Proper generalized decomposition, Lead, numerical method
is an iterative numerical method for solving boundary value problems
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