Dismiss
InnovationQ will be updated on Sunday, Oct. 22, from 10am ET - noon. You may experience brief service interruptions during that time.
Browse Prior Art Database

# 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

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

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 100% of the total text.

Page 1 of 2

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.

1

Page 2 of 2

2