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Theory of numerical analysis

  Theory of numerical analysis The following is a rough categorization of the mathematical theory underlying numerical analysis, keeping in mind that there is often a great deal of overlap between the listed areas. Numerical linear and  nonlinear algebra Many problems in applied  mathematics  involve solving systems of linear equations, with the linear system occurring naturally in some cases and as a part of the solution process in other cases. Linear systems are usually written using matrix-vector notation,  A x  =  b  with  A  the  matrix  of coefficients for the system,  x  the column  vector  of the unknown variables  x 1 ,…,  x n , and  b  a given column  vector . Solving linear systems with up to 1,000 variables is now considered relatively straightforward in most cases. For small to moderately sized linear systems (say,  n  ≤ 1,000), the favoured numerical meth...
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numerical methods

  Numerical analysis mathematics Print   Cite   Share   Feedback   Alternate titles: numerical methods, quantitative analysis Written by  Kendall E. Atkinson Fact-checked by   The Editors of Encyclopaedia Britannica Last Updated:  Article History Key People:   James H. Wilkinson   William Kahan Related Topics:   mathematics   finite element method   finite difference method See all related content → Summary Read a brief summary of this topic numerical analysis , area of  mathematics  and  computer science  that creates, analyzes, and  implements   algorithms  for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of  digital computers  has led to an increasing use of realistic  math...
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Computing values of functions

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  Areas of study [ edit ] The field of numerical analysis includes many sub-disciplines. Some of the major ones are: Computing values of functions [ edit ] Interpolation: Observing that the temperature varies from 20 degrees Celsius at 1:00 to 14 degrees at 3:00, a linear interpolation of this data would conclude that it was 17 degrees at 2:00 and 18.5 degrees at 1:30pm. Extrapolation: If the  gross domestic product  of a country has been growing an average of 5% per year and was 100 billion last year, it might extrapolated that it will be 105 billion this year. Regression: In linear regression, given  n  points, a line is computed that passes as close as possible to those  n  points. Optimization: Suppose lemonade is sold at a  lemonade stand , at $1.00 per glass, that 197 glasses of lemonade can be sold per day, and that for each increase of $0.01, one less glass of lemonade will be sold per day. If $1.485 could be charged, profit would be maxim...
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