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Appendix D

A Detailed Look at _

Section 13, Finding the Roots of an Equation, includes the basic

information needed for the effective use of the _ algorithm. This

appendix presents more advanced, supplemental considerations regarding

How _ Works

You will be able to use _ most effectively by having a basic

understanding of how the algorithm works.

In the process of searching for a zero of the

specified function, the algorithm uses the

value of the function at two or three

previous estimates to approximate the shape



      

estimate where the graph might cross the x-

axis. The function subroutine is then

executed, computing the value of the

function at the new estimate. This procedure is performed repeatedly by the

_ algorithm.

If any two estimates yield function values

with opposite signs, the algorithm presumes

that the function's graph must cross the x-

axis in at least one place in the interval

between these estimates. The interval is

systematically narrowed until a root of the

equation is found.

A root is successfully found either if the

computed function value is equal to zero or

if two estimates, differing by one unit in their last significant digit, give

function values having opposite signs. In this case, execution stops and the

estimate is displayed.

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HP 15C User Manual Page 220