Branches of Mathematics
Numerical Analysis
Also Known As Numerical Methods
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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.
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 Cross-Tradition Connections
Sources
1. Numerical Analysis (Wikipedia)
Wikimedia Foundationlead paragraphQuote, lead paragraph
Numerical analysis is the study of algorithms for the problems of continuous mathematics.
1. Numerical Analysis (Wikipedia)
Wikimedia Foundationbody textQuote, 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
1. Numerical Analysis (Wikipedia)
Wikimedia Foundationbody text on stabilityQuote, 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.
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