DR.K.JIVIGAN

  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...

  Discretization [ edit ] Furthermore, continuous problems must sometimes be replaced by a discrete problem whose solution is known to approximate that of the continuous problem; this process is called ' discretization '. For example, the solution of a  differential equation  is a  function . This function must be represented by a finite amount of data, for instance by its value at a finite number of points at its domain, even though this domain is a  continuum . Generation and propagation of errors [ edit ] The study of errors forms an important part of numerical analysis. There are several ways in which error can be introduced in the solution of the problem. Round-off [ edit ] Round-off errors  arise because it is impossible to represent all  real numbers  exactly on a machine with finite memory (which is what all practical  digital computers  are). Truncation and discretization error [ edit ] Truncation errors  are committed when...