{"id":26337,"date":"2017-10-26T21:05:03","date_gmt":"2017-10-26T15:35:03","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=26337"},"modified":"2017-10-26T21:05:03","modified_gmt":"2017-10-26T15:35:03","slug":"c-programming-program-newton-raphson-method","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/c-programming-program-newton-raphson-method\/","title":{"rendered":"C++ Programming – Program for Newton Raphson Method"},"content":{"rendered":"

Given a function f(x) on floating number x and an initial guess for root, find root of function in interval. Here f(x) represents algebraic or transcendental equation.<\/p>\n

For simplicity, we have assumed that derivative of function is also provided as input.<\/p>\n

Example:<\/p>\n

Input: A function of x (for example x3 \u2013 x2 + 2),
\nderivative function of x (3\u00d72 \u2013 3x for above example)
\nand an initial guess x0 = -20
\nOutput: The value of root is : -1.00
\nOR any other value close to root.
\nWe have discussed below methods to find root in set 1 and set 2
\nSet 1: The Bisection Method
\nSet 2: The Method Of False Position<\/p>\n

Comparison with above two methods:<\/p>\n

In previous methods, we were given an interval. Here we are required an initial guess value of root.
\nThe previous two methods are guaranteed to converge, Newton Rahhson may not converge in some cases.
\nNewton Raphson method requires derivative. Some functions may be difficult to
\nimpossible to differentiate.
\nFor many problems, Newton Raphson method converges faster than the above two methods.
\nAlso, it can identify repeated roots, since it does not look for changes in the sign of f(x) explicitly
\nThe formula:
\nStarting from initial guess x1, the Newton Raphson method uses below formula to find next value of x, i.e., xn+1 from previous value xn.<\/p>\n

\"nrm\"<\/p>\n

Algorithm:<\/strong>
\nInput: initial x, func(x), derivFunc(x)
\nOutput: Root of Func()<\/p>\n

    \n
  1. Compute values of func(x) and derivFunc(x) for given initial x<\/li>\n
  2. Compute h: h = func(x) \/ derivFunc(x)<\/li>\n
  3. While h is greater than allowed error \u03b5\n
      \n
    1. h = func(x) \/ derivFunc(x)<\/li>\n
    2. x = x \u2013 h<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n[ad type=\u201dbanner\u201d]\n

      Below is C++ implementation of above algorithm.<\/p>\n[pastacode lang=\u201dcpp\u201d manual=\u201d%2F%2F%20C%2B%2B%20program%20for%20implementation%20of%20Newton%20Raphson%20Method%20for%0A%2F%2F%20solving%20equations%0A%23include%3Cbits%2Fstdc%2B%2B.h%3E%0A%23define%20EPSILON%200.001%0Ausing%20namespace%20std%3B%0A%20%0A%2F%2F%20An%20example%20function%20whose%20solution%20is%20determined%20using%0A%2F%2F%20Bisection%20Method.%20The%20function%20is%20x%5E3%20-%20x%5E2%20%20%2B%202%0Adouble%20func(double%20x)%0A%7B%0A%20%20%20%20return%20x*x*x%20-%20x*x%20%2B%202%3B%0A%7D%0A%20%0A%2F%2F%20Derivative%20of%20the%20above%20function%20which%20is%203*x%5Ex%20-%202*x%0Adouble%20derivFunc(double%20x)%0A%7B%0A%20%20%20%20return%203*x*x%20-%202*x%3B%0A%7D%0A%20%0A%2F%2F%20Function%20to%20find%20the%20root%0Avoid%20newtonRaphson(double%20x)%0A%7B%0A%20%20%20%20double%20h%20%3D%20func(x)%20%2F%20derivFunc(x)%3B%0A%20%20%20%20while%20(abs(h)%20%3E%3D%20EPSILON)%0A%20%20%20%20%7B%0A%20%20%20%20%20%20%20%20h%20%3D%20func(x)%2FderivFunc(x)%3B%0A%20%20%0A%20%20%20%20%20%20%20%20%2F%2F%20x(i%2B1)%20%3D%20x(i)%20-%20f(x)%20%2F%20f'(x)%20%20%0A%20%20%20%20%20%20%20%20x%20%3D%20x%20-%20h%3B%0A%20%20%20%20%7D%0A%20%0A%20%20%20%20cout%20%3C%3C%20%22The%20value%20of%20the%20root%20is%20%3A%20%22%20%3C%3C%20x%3B%0A%7D%0A%20%0A%2F%2F%20Driver%20program%20to%20test%20above%0Aint%20main()%0A%7B%0A%20%20%20%20double%20\u00d70%20%3D%20-20%3B%20%2F%2F%20Initial%20values%20assumed%0A%20%20%20%20newtonRaphson(x0)%3B%0A%20%20%20%20return%200%3B%0A%7D\u201d message=\u201dC++ Program\u201d highlight=\u201d\u201d provider=\u201dmanual\u201d\/]\n

      Output:<\/p>\n

      The value of root is : -1.00<\/pre>\n[ad type=\u201dbanner\u201d]\n","protected":false},"excerpt":{"rendered":"
      C++ Programming – Program for Newton Raphson Method – Mathematical Algorithms – Given a function f(x) on floating number x and an initial guess for root<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[69969,83515,1,74058,83622],"tags":[78396,77752,78282,78269,78390,78397,78406,78392,77771,78403,78395,78391,78387,78398,78409,78388,78410,78393,78416,78274,78405,78402,78389,78407,78386,78414,78400,77769,78408,78289,78411,78283,78404,77004,78266,78276,78288,78412,78284,78399,78401,78413,76990,78295,78394,77757,76998,77011,78272,78415],"class_list":["post-26337","post","type-post","status-publish","format-standard","hentry","category-algorithm","category-c-programming-3","category-coding","category-mathematical-algorithms","category-newton-raphson-method","tag-applied-numerical-methods-with-matlab-pdf","tag-bisection-method-c-program","tag-c-program-for-bisection-method","tag-c-program-of-bisection-method","tag-find-square-root","tag-fortran-program-for-newton-raphson-method","tag-gauss-jacobi-method-c-program","tag-how-to-solve-newton-raphson-method","tag-introduction-to-numerical-analysis-pdf","tag-matlab-program-for-newton-raphson-method","tag-newton-formula","tag-newton-raphson","tag-newton-raphson-formula","tag-newton-raphson-fortran-code","tag-newton-raphson-matlab-program","tag-newton-raphson-method","tag-newton-raphson-method-code","tag-newton-raphson-method-example","tag-newton-raphson-method-example-solution","tag-newton-raphson-method-formula","tag-newton-raphson-method-fortran","tag-newton-raphson-method-problems-and-solutions","tag-newton-raphson-method-theory","tag-newtons-method-calculus","tag-newtons-method-calculator","tag-numerical-analysis-and-computer-programming-pdf","tag-numerical-analysis-book-pdf","tag-numerical-analysis-pdf","tag-numerical-analysis-programming-in-c-pdf","tag-numerical-methods-c-programs","tag-numerical-methods-in-c-pdf","tag-numerical-methods-in-c-programming","tag-numerical-methods-in-c-programming-pdf","tag-numerical-methods-pdf","tag-numerical-methods-programs-in-c","tag-numerical-methods-using-c-programming","tag-numerical-methods-with-programs-in-c","tag-numerical-programming","tag-numerical-programming-in-c","tag-numerical-recipes-in-c-pdf","tag-numerical-recipes-pdf","tag-program-for-newton-raphson-method","tag-program-of-bisection-method-in-c-language","tag-program-of-newton-raphson-method-in-c","tag-raphson-method","tag-sample-c-programs-pdf","tag-secant-method-example-solved","tag-secant-method-formula","tag-simple-c-program-for-bisection-method","tag-what-is-the-newton-raphson-method"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/comments?post=26337"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26337\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=26337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=26337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=26337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}