HP 15c Collector's Edition User Manual

238 Appendix D: A Detailed Look at _
 Examine the behavior of the deflated function at x-values near the
known root. If the function’s calculated values cross the x-axis
smoothly, either another root or a greater multiplicity is indicated.
 Analyze the original function and its derivatives algebraically. It
may be possible to determine its behavior for x-values near the
known root. (A Taylor series representation, for example, may
indicate the multiplicity of a root.)
Limiting the Estimation Time
Occasionally, you may desire to limit the time used by _ to find a
root. You can use two possible techniques to do this—counting iterations
and specifying a tolerance.
Counting Iterations
While searching for a root, _ typically samples your function at
least a dozen times. Occasionally, _ may need to sample it one
hundred times or more. (However, _ will always stop by itself.)
Because your function subroutine is executed once for each estimate that
is tried, it can count and limit the number of iterations. An easy way to do
this is with an I instruction to accumulate the number of iterations in
the Index register (or other storage register).
If you store an appropriate number in the register before using _,
your subroutine can interrupt the _ algorithm when the limit is
exceeded.
Specifying a Tolerance
You can shorten the time required to find a root by specifying a tolerable
inaccuracy for your function. Your subroutine should return a function
value of zero if the calculated function value is less than the specified
tolerance. This tolerance that you specify should correspond to a value
that is negligible for practical purposes or should correspond to the
accuracy of the computation. This technique eliminates the time required
to define the estimate more accurately than is justified by the problem.
(The example on page 224 uses this method.)

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.