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Extrema of Cubics Over an Interval

IP.com Disclosure Number: IPCOM000077993D
Original Publication Date: 1972-Oct-01
Included in the Prior Art Database: 2005-Feb-25
Document File: 2 page(s) / 53K

Publishing Venue

IBM

Related People

Dimsdale, B: AUTHOR

Abstract

Given the cubic z = au/3/+ bu/2/+ cu + d, the objective is to find locations and values of extrema (maximum and minimum) within the interval O

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Extrema of Cubics Over an Interval

Given the cubic z = au/3/+ bu/2/+ cu + d, the objective is to find locations and values of extrema (maximum and minimum) within the interval O<u<1 irrespective of size of coefficients. The principle requirement is speed.

With the boxes as numbered in the flow diagram there are, for a<0, eleven possible paths through the flow diagram as follows: 1,2,3,4,5,6,7,18,8 1,2,10,11,8 1,2,10,12,5 1,2,3,13,14,15,16,8 1,2,3,13,14,17,16,8 1,2,3,13,11,8 1,2,3,4,12,8 1,2,3,4,5,12,8 1,2,3,4,5,6,19,20,8 1,2,3,4,5,6,19,17,16,8 1,2,3,4,5,6,7,11,8

For a<0, there are also eleven paths, with 1,2 replaced by 1,9,2 and 8 replaced by 8,21. Along each path there are two more comparisons for a<0. These 22 paths encompass every possible case.

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