Cited by 2.9k
This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.
Australian National University
ORCID: 0000-0002-8495-7437Publishes on Coding theory and cryptography, Numerical Methods and Algorithms, Matrix Theory and Algorithms. 362 papers and 12.4k citations.
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This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.
It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 n + 10( n - 1)/ p using p ≥ 1 processors which can independently perform arithmetic operations in unit time. This bound is within a constant factor of the best possible. A sharper result is given for expressions without the division operation, and the question of numerical stability is discussed.
An algorithm is presented for finding a zero of a function which changes sign in a given interval. The algorithm combines linear interpolation and inverse quadratic interpolation with bisection. Convergence is usually superlinear, and is never much slower than for bisection. ALGOL 60 procedures are given.