function project$\_9()$

PROJECT$\_9$ project$\_9()$ is the driver function for the program.

$\%$

Name:

$ Date:

$\%$ Class: CMPSC $200$

Description: Approximate the zero of a function using the

$x$ Newton$-$Raphson Method.

$\%$ Print the splash screen $-$ you need to add the print header yourself

$ Create an anonymous function by calling the get$\_$function$()$ function

Use the get data function three times to enter the three inputs:

$\%,xa,$ and $b$

$\%x0$ is the starting value

$\%$ a is the minimum $($it is only for the plot at the end$)$

$\%$ b is the maximum $($it is also only for the plot at the end$)$

In the get$\_$data function you must use check$\_$data to error check

inputs. If a and $b$ are not

In the correct range the check data function will return $1,$ and in

get$\_$data the function will be called again recursively $=$ this

is an important aspect of the program

The restrictions on the inputs should be

xo can be any value

starting$\_$point, a$,$ must be less than xin

stopping.point, $b,$ must be greater than $x$

$\%$ Call get$\_$zero to estimate the zero

$x$ zero $=$get zero $(f,x)$:

$6$ Print results from the previous function $-$ create and then call

$\%$ a print$-$results function. This function will have three input variables

$\%$ the function handle

$\%-$ the starting point, xo

$\%-$ the zero point $=$ in this program $x$ zero

GET$\_$ZERO $x=$ get zero $(f,x)$ determines the zero of the function $f$

Name: :

Date:

Class:

CMPSC $200$

$\%$ Set value eps

$\%$ Should be small but reasonable. About $0,0001$ works well

$6$ Check if eps$).$ If it is then update $x$ using

the Newton $-$ Raphson and then call get zero again with the same

function but the new $$ value.

and

function plot, function, zero$($func$,x$ point, minx, maxx $)$

$8$ PLOT FUNCTION,ZERD plot function,zero$($func$,$ min, maxx, xPoint$)$ plots

$4$ the function passed in func between the minimum and maximum values

$8$ Indicated. It then plots a point at the zero of the function with a $4$

cross at that point.

$\%.$ Name:

Class: CMPSC $200$

Date: March $19,2019$

$\%$

Create a vector of points from min to max

$x=$ Linspace $,$ max, $250$

& Finish with the title and axes labels

title $($func$2$str $($func$))$:

$x$ labe l$\text{'}(x\text{'})$:

ylabel$(\text{'}{y}^{\text{'}}\text{'})$;

hold off $\%$ return the hold to the default

end

$$ using this template in matlab do the following project

Objective Using MatLab Recursive Functions.

Project In the Calculus we study the Newton$-$Raphson method for solving equations. This technique uses the value of a function and its derivative to estimate where the function crosses the $x$ axis. If necessary it repeats the process until the amount of change in the estimate is smaller than some predetermined amount.

The formula is

$x_{n+1}=x_n-\frac{f(x_n)}{f^{\text{'}}(x_n)}$

You will write a program that uses a recursive function to perform this operation estimating where a function crosses the $x-$axis.

Methodology

Prompt the user for the mathematical function that you want to solve.

Prompt the user for the starting value. Call this $x0.$

In the get$\_$zero function you will set a differential value. Call this dx$.$ It should be a small value, say $dx=0\mathrm{.}01.$

In the get$\_$zero function you will set a stopping criteria. Call this eps. It should be a small value, say eps $=0\mathrm{.}001.$

Call the get$\_$zero function. You will pass the function and the starting value for the zero of the function. The function will return a new value for the zero.

In the get$\_$zero function calculate a new value for $x0$ by evaluating the function and an estimate of the derivative at $x.$

Compare $|f(x)|$ to eps.

If $|f(x)|>$ eps then call get$\_$zero from the selection structure. You pass the same function and the same variable, but now $x$ contains the new predicted value for the intercept.

If If $|f(x)|$ eps the function returns the calculated intercept value.

Call print$\_$results to show the function, the starting value, and the estimated zero. An example of what the output might look like is

$\backslash$ta