Showing posts with label Numerical Methods. Show all posts
Showing posts with label Numerical Methods. Show all posts

Newton Raphson Method

#  Newton Raphson Method
# The Newton-Raphson method (also known as Newton's method) is a way
# to quickly find a good approximation for the root of a real-valued function

xcube=int(input('Enter the values for Xcube: '))

xsquare=int(input('Enter the values for Xsquare: '))

x=int(input('Enter the values for X: '))

constant=int(input('Enter the values for Constant: '))

X0=int(input('Enter the values for inital vaule X0: '))
 # It can be any value, but based on the incorrectness the root convergence
 #  will delay. Here we can use trail and error method for input value.
X1= X0-((((xcube*X0*X0*X0)+(xsquare*X0*X0)+(x*X0)+constant)/((xcube*3*X0*X0)+(xsquare*2*X0)+x)))

print ("Root at first approximations:",X1)

X2= X1-((((xcube*X1*X1*X1)+(xsquare*X1*X1)+(x*X1)+constant)/((xcube*3*X1*X1)+(xsquare*2*X1)+x)))

print ("Root at second approximations:",X2)

X3= X2-((((xcube*X2*X2*X2)+(xsquare*X2*X2)+(x*X2)+constant)/((xcube*3*X2*X2)+(xsquare*2*X2)+x)))

print ("Root at thrid approximations:",X3)

X4= X3-((((xcube*X3*X3*X3)+(xsquare*X3*X3)+(x*X3)+constant)/((xcube*3*X3*X3)+(xsquare*2*X3)+x)))

print ("Root at fourth approximations:",X4)

X5= X4-((((xcube*X4*X4*X4)+(xsquare*X4*X4)+(x*X4)+constant)/((xcube*3*X4*X4)+(xsquare*2*X4)+x)))

print ("Root at fifth approximations:",X5)