An unrestricted algorithm is an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

for the computation of a mathematical function that puts no restrictions on the range of the

argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...

or on the precision that may be demanded in the result. The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980. In the problem of developing algorithms for computing, as regards the values of a real-valued function of a real variable (e.g., ''g'' 'x''in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on the

real line In elementary mathematics, a number line is a picture of a graduated straight line (geometry), line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real ...

would also be specified for values when the values of a function are to be evaluated. Different algorithms may have to be applied for evaluating functions outside the interval. An unrestricted algorithm envisages a situation in which a user may stipulate the value of ''x'' and also the precision required in ''g''(''x'') quite arbitrarily. The algorithm should then produce an acceptable result without failure.

References

{{reflist Numerical analysis * Theoretical computer science