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Branches of Mathematic

Numerical Analysis

Also Known As Numerical Methods
Computation, Optimization and Control

Numerical analysis is the study of algorithms for the problems of continuous mathematics. It develops methods that obtain approximate solutions within controlled, known error bounds for problems that are impractical or impossible to solve exactly by symbolic methods. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Central Question
How can a problem of continuous mathematics be solved by an algorithm that produces an approximate answer within a controlled, known error bound? 1
Key Debate
A central working tension in the field is controlling how errors compound during a calculation: an algorithm is called numerically stable only if an error, whatever its cause, does not grow to be much larger as the calculation proceeds, which drives much of the field's method design. 1
Classification
Pure or Applied
Applied Mathematics 1
Numerical Analysis
Filter Results1 entry

Condition Number

Numerical Analysis
Connections

Associated With

Approximation Theory, Branches of Mathematics

In Branch

Applied and Computational Mathematics, Branches of Mathematics
Source Numerical Analysis (Wikipedia)

Includes

Bernstein Polynomial, Theorems
Source Bernstein Polynomial (Wikipedia)
Condition Number, Mathematical Objects
Source Condition Number (Wikipedia)
George Polya, Mathematicians
Source George Pólya (Wikipedia)
Sources
1. Numerical Analysis (Wikipedia)
Wikimedia Foundation
  • lead paragraph
    Numerical analysis is the study of algorithms for the problems of continuous mathematics.
  • body text
    rather than giving exact symbolic answers translated into digits and applicable only to real-world measurements, approximate solutions within specified error bounds are used
  • body text on stability
    An algorithm is called numerically stable if an error, whatever its cause, does not grow to be much larger during the calculation.
  • Applications section
    Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.
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Bernstein Polynomial (Wikipedia)
Includes: Bernstein Polynomial, Lead sentence
Quote, Includes: Bernstein Polynomial, Lead sentence
In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Berns
View the Source
Condition Number (Wikipedia)
Includes: Condition Number, Lead sentence
Quote, Includes: Condition Number, Lead sentence
In numerical analysis, the condition number of a function measures how much the output value of the function can change for a smal
View the Source
George Pólya (Wikipedia)
Includes: George Polya, Lead paragraph [in-branch 4]
Quote, Includes: George Polya, Lead paragraph [in-branch 4]
numerical analysis
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