The function ScanForRoots to scan a given function f(x) for it’s roots using the newton’s algorithm.
engineering
Description
Project 1
Please develop the function ScanForRoots to scan a given function f(x) for it’s roots using the newton’s
algorithm.
The Interface
The program should read the following input parameters from an input file. The file’s format is given as
follows.
1 [max number of roots to find]
2 [lower bound: lb] [upper bound: up] [step width: sw]
3 [precision eps] [step width h] [max iteration: ix]
The program should search the root of a function with the starting position x0. The starting position x0
should be taken from the interval which is described by the parameters ub, lb and sw read from the input
file. The found roots of the function should be saved in an dynamical array, which should be a parameter
of the function ScanForRoots The size of the array should be set by a parameter, which is read from the
input file.
An example data file is given below.
1 10
2 -10. +10. 0.1
3 1.e-7 0.01 100
In the project a reasonable interval should be selected to be able to check the quality of the developed
software.
The Function ScanForRoots
So the interface to Scan For Roots is the following.
integer function ScanForRouts(f,lb,ub,sw,eps,h,maxit,roots)
Parameter Type Comment
f function function to analyse
lb real(8) lower bound of search interval
ub real(8) upper bound of search interval
sw real(8) step width for the starting position x0
eps real(8) precision for the newton algorithm
maxit integer maximal number of iteration for one root search
roots real(8) one indexed array for the found roots
The return value of ScanForRoots should give the number of found roots. The roots should not be stored
multiple.
The main program which should call ScanForRoots should do the following.
• open, read and close the input file ScanForRoots.inp.
• call ScanForRoots1
to search for the function’s roots.
• write a little report which gives a list of the found roots
