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...