Survey of Numerical Mathematics: v. 2 - ISBN:020108774X

Survey of Numerical Mathematics: v. 2

Date: 09 April 2011, 13:20

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Since the advent of automatic digital computers there has been a rapid development of the branch of applied mathematics known as numerical analysis. Numerical analysis is concerned with the development, analysis, and evaluation of numerical algorithms which can be carried out on a computer (usually an automatic digital computer) for obtaining numerical solutions to mathematical problems. Although the methods and results of classical analysis can often be helpful, they usually provide only background and/or a starting point for the numerical analyst. For example, the pure mathematician may be fully satisfied if he can prove that a unique solution to a given problem exists, but it is up to the numerical analyst to devise a procedure for actually computing a solution to within a specified accuracy and within a reasonable time. In developing an algorithm to use in solving a given problem, the numerical analyst must be concerned not only with the number of arithmetic operations and the theoretical accuracy but also with the cumulative effects of rounding errors which are made when the algorithm is implemented on a computer.

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