Even when solving finite systems of linear equations by direct numerical methods, infinite precision arithmetic is needed in order to find a particular exact solution. ... When approximating a problem, a numerical analyst would want to understand the behaviour of the error in the computed solution.

Why do you need methods of approximations?

Approximation Methods Can be Used When Exact Solutions to the Schrödinger Equation Can Not be Found. ... It has therefore proven essential to develop and efficiently implement mathematical methods which can provide approximate solutions to such eigenvalue equations.

What do you mean by approximation in numerical analysis?

The approximating equation has a solution at a discrete set of points, and this solution approximates that of the original equation. Such numerical procedures are often called finite difference methods.