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 QuestionHow can a problem of continuous mathematics be solved by an algorithm that produces an approximate answer within a controlled, known error bound? 1 Key DebateA 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 Connections
Associated With
In Branch
Source Numerical Analysis (Wikipedia)
Includes
Source MacTutor biography of Alston Householder, St Andrews
Source Bernstein Polynomial (Wikipedia)
Source Carl Runge, Biography (MacTutor History of Mathematics)
Source Condition Number (Wikipedia)
Source George Pólya (Wikipedia)
Source Martin Kutta, Biography (MacTutor History of Mathematics)
Source Michel Crouzeix (Mathematics Genealogy Project)
Source MacTutor History of Mathematics: Semyon Gershgorin
Sources
1. Numerical Analysis (Wikipedia)
Wikimedia Foundationlead 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.
View the Source Michel Crouzeix (Mathematics Genealogy Project)
Includes: Michel Crouzeix, Degree recordQuote, Includes: Michel Crouzeix, Degree record
Numerical analysis
MacTutor History of Mathematics: Semyon Gershgorin
Includes: Semyon Aranovich Gershgorin, Biography textQuote, Includes: Semyon Aranovich Gershgorin, Biography text
Semyon Gershgorin was a Belarussian mathematician who produced important results in numerical approximation
Bernstein Polynomial (Wikipedia)
Includes: Bernstein Polynomial, Lead sentenceQuote, 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
Condition Number (Wikipedia)
Includes: Condition Number, Lead sentenceQuote, 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
George Pólya (Wikipedia)
Includes: George Pólya, Lead paragraph [in-branch 4]Quote, Includes: George Pólya, Lead paragraph [in-branch 4]
numerical analysis
MacTutor biography of Alston Householder, St Andrews
Includes: Alston Householder, SummaryQuote, Includes: Alston Householder, Summary
Alston Householder was an American mathematician who worked in mathematical biology and numerical analysis.
Carl Runge, Biography (MacTutor History of Mathematics)
Includes: Carl Runge, SummaryQuote, Includes: Carl Runge, Summary
Carl Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements.
Martin Kutta, Biography (MacTutor History of Mathematics)
Includes: Martin Kutta, SummaryQuote, Includes: Martin Kutta, Summary
Wilhelm Kutta was a German engineer who is best known for his work on the numerical solution of differential equations ( the Runge-Kutta method ) .
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