Approximation theory: Difference between revisions
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In [[mathematics]], '''approximation theory''' is concerned with how [[Function (mathematics)|functions]] can be best [[approximation|approximated]] with simpler functions, and with quantitatively characterising the [[approximation error|errors]] introduced thereby. What is meant by ''best'' and ''simpler'' will depend on the application. | In [[mathematics]], '''approximation theory''' is concerned with how [[Function (mathematics)|functions]] can be best [[approximation|approximated]] with simpler functions, and with quantitatively characterising the [[approximation error|errors]] introduced thereby. What is meant by ''best'' and ''simpler'' will depend on the application. | ||
Approximation theory has many applications, especially in [[numerical computation]], [[physics]], [[engineering]] and [[computer science]]. Of particular interest in [[computer science]] is approximating functions in a computer mathematical library, using operations that can be performed on the computer (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational approximations. | Approximation theory has many applications, especially in [[numerical computation]], [[physics]], [[engineering]] and [[computer science]]. Of particular interest in [[computer science]] is approximating functions in a computer mathematical library, using operations that can be performed on the computer (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational approximations. | ||
Revision as of 10:28, 14 July 2008
In mathematics, approximation theory is concerned with how functions can be best approximated with simpler functions, and with quantitatively characterising the errors introduced thereby. What is meant by best and simpler will depend on the application.
Approximation theory has many applications, especially in numerical computation, physics, engineering and computer science. Of particular interest in computer science is approximating functions in a computer mathematical library, using operations that can be performed on the computer (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational approximations.