The ever-growing relevance of computers to our daily lives increases the importance of developing algorithms suitable for computer use. This outstanding volume for graduate students and research workers proposes improvements to existing algorithms extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Subjects include the use of successive interpolation for finding simple zeros of a function and its derivatives; an algorithm with guaranteed convergence for finding a minimum of a function of one variable; global minimization given an upper bound on the second derivative; and a new algorithm for minimizing a function of several variables without calculating derivatives. Many numerical examples appear here, along with a complete analysis of the rate of convergence for most of the algorithms and error bounds that allow for the effect of rounding errors.