Merge pull request #1 from prashantsinalkar/masterHEADmaster

Added R TBC

1 files changed, 54 insertions, 0 deletions

diff --git a/Numerical_Methods_by_E_Balaguruswamy/CH6/EX6.7/Ex6_7.R b/Numerical_Methods_by_E_Balaguruswamy/CH6/EX6.7/Ex6_7.R
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+# Example 7     Chapter 6       Page no.: 147

+# Newton-Raphson Method

+

+install.packages("numDeriv")

+library("numDeriv")

+

+# Given Function

+u <- function(x) {

+  x^2-3*x+2

+}

+

+curve(u, xlim=c(-5,5), col='blue', lwd=2, lty=2, ylab='f(x)')

+abline(h=0)

+abline(v=0)

+

+# From the curve the points in the vicinity are noted

+a <- 0

+b <-1

+

+newton.raphson <- function(f, a, b, tol = 1e-5, n = 1000) {

+  require(numDeriv) # Package for computing f'(x)

+  

+  x0 <- a # Set start value to supplied lower bound

+  k <- n # Initialize for iteration results

+  

+  # Check the upper and lower bounds to see if approximations result in 0

+  fa <- f(a)

+  if (fa == 0.0) {

+    return(a)

+  }

+  

+  fb <- f(b)

+  if (fb == 0.0) {

+    return(b)

+  }

+  

+  for (i in 1:n) {

+    dx <- genD(func = f, x = x0)$D[1] # First-order derivative f'(x0)

+    x1 <- x0 - (f(x0) / dx)

+    k[i] <- x1 

+    # Checking difference between values

+    if (abs(x1 - x0) < tol) {

+      root.approx <- tail(k, n=1)

+      res <- list('root approximation' = root.approx, 'iterations' = k)

+      return(res)

+    }

+    # If Newton-Raphson has not yet reached convergence set x1 as x0 and continue

+    x0 <- x1

+  }

+  print('Too many iterations in method')

+}

+

+N <- newton.raphson(u, a, b)

+cat("The root closer to the point x=0 is",N)
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