ABSTRACT. 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 log2n + 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.
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