Newton-Raphson Method of Solving a Nonlinear Equation More Examples: Computer Science

03.04.2

Chapter 03.04

Newton-Raphson More Examples: Computer Science 03.04.3

Chapter 03.04

Newton-Raphson Method of Solving a Nonlinear Equation More ExamplesComputer ScienceExample 1To find the inverse of a number , one can use the equation

where is the inverse of .

Use the Newton-Raphson method of finding roots of equations to find the inverse of . Conduct three iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration.

Solution

Let us take the initial guess of the root of as .Iteration 1

The estimate of the root is

=

The absolute relative approximate error at the end of Iteration 1 is

The number of significant digits at least correct is 0, as you need an absolute relative approximate error of less than for one significant digit to be correct in your result.

Iteration 2

The estimate of the root is

=

The absolute relative approximate error at the end of Iteration 2 is

The number of significant digits at least correct is 0.

Iteration 3

The estimate of the root is

=

The absolute relative approximate error at the end of Iteration 3 is

Hence the number of significant digits at least correct is given by the largest value of for which

So

The number of significant digits at least correct in the estimated root 0.39999 is 2.NONLINEAR EQUATIONS

TopicNewton-Raphson Method-More Examples

SummaryExamples of Newton-Raphson Method

MajorComputer Engineering

AuthorsAutar Kaw

DateOctober 4, 2013

Web Sitehttp://numericalmethods.eng.usf.edu

03.04.1

_1288899821.unknown

_1306147251.unknown

_1306148073.unknown

_1306148187.unknown

_1306148247.unknown

_1306148312.unknown

_1306148326.unknown

_1306148266.unknown

_1306148232.unknown

_1306148110.unknown

_1306147972.unknown

_1306148010.unknown

_1306147274.unknown

_1306144690.unknown

_1306144895.unknown

_1306147088.unknown

_1306144760.unknown

_1288899860.unknown

_1288899904.unknown

_1288899938.unknown

_1288899955.unknown

_1288899916.unknown

_1288899878.unknown

_1288899835.unknown

_1288899841.unknown

_1288899373.unknown

_1288899736.unknown

_1288899763.unknown

_1288899805.unknown

_1288899755.unknown

_1288899757.unknown

_1288899380.unknown

_1288899612.unknown

_1288899376.unknown

_1288896449.unknown

_1288899363.unknown

_1288899368.unknown

_1288896529.unknown

_1288896423.unknown

_1288896431.unknown

_1288896417.unknown

_1093125011.unknown