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# High Speed Search Algorithm

IP.com Disclosure Number: IPCOM000082524D
Original Publication Date: 1974-Nov-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 57K

IBM

## Related People

Micchelli, CA: AUTHOR [+2]

## Abstract

If f has a simple root in (0,1) the algorithms A(r), r = 1, 2 determine a nested sequence of intervals (x1(j), x2(j)), j = 1, 2, ..., each member of which contains the root of f. Take (x1(1), x2(1)) = (0,1) and assume for definiteness that f(x1(1)) < 0 < f(x2(1)). The algorithms proceed until |x1(j)-x2(j)| is less that a prescribed tolerance, e.

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High Speed Search Algorithm

If f has a simple root in (0,1) the algorithms A(r), r = 1, 2 determine a nested sequence of intervals (x1(j), x2(j)), j = 1, 2, ..., each member of which contains the root of f. Take (x1(1), x2(1)) = (0,1) and assume for definiteness that f(x1(1)) < 0 < f(x2(1)). The algorithms proceed until |x1(j)-x2(j)| is less that a prescribed tolerance, e.

The algorithms are described to operate on the following class of functions

n(m,M) = { f | m<= f(n) (x) <= M, xe[0,1]},

and are described by the following flow chart:

(Image Omitted)

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