Fortran program for secant method numerical
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This very important when user interaction is involved. The fprintf function allows you to "write" information to the screen for the user to view.
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The algorithm is robust and commonly used in libraries with a roots() function built in.Fprintf. It has a guaranteed run time equal to that of the bisection method (which always converges in a known number of steps (log2 steps to be precise ) unlike the other methods), but the algorithm uses the much faster inverse quadratic interpolation and secant method whenever possible. Abs (c - d ) * 0.5 ) ) ) ||ĭouble step = 0.001 // Smaller step values produce more accurate and precise resultsīrent's Method uses a combination of the bisection method, inverse quadratic interpolation, and the secant method to find roots. Public static double BrentsFun (Func f, double lower, double upper, double tol, uint maxIter )ĭouble fa = f (a ) // calculated now to save function callsĭouble fb = f (b ) // calculated now to save function calls Private static void Swap ( ref T a, ref T b ) Roots (f ,x1 ,x2 ,step ,tol ) ĭouble root = BrentsFun (f, lower : - 1.0, upper : 4, tol : 0.002, maxIter : 100 )
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XYRES first result = find root (f, LENG -1.0, LENG 3.0, EMPTY, EMPTY ) PROC f = (DBL x )DBL : x UP 3 - LONG 3.1 * x UP 2 + LONG 2.0 * x ĭBL first root, second root, third root # WHILE # ABS dx > x error AND ABS dy > y error DO X1 := x2 y1 := y2 # retain for next iteration # XY (x1, y1 ) # we already have a solution! # Y error := (in y error | (DBL y error ) :y error | small real ) X error := (in x error | (DBL x error ) :x error | small real ) , INT limit = ENTIER ( long real width / log (2 ) ) # worst case of a binary search) #ĭBL x1 := (in x1 | (DBL x1 ) :x1 | -5.0 ), # if x1 is EMPTY then -5.0 # PROC find root = ( PROC (DBL )DBL f, DBLOPT in x1, in x2, in x error, in y error )XYRES : ( Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tinyįORMAT dbl = $g ( - long real width, long real width -6, -2 )$ įORMAT xy root = $f (dbl ) " ("b ( "Exactly", "Approximately" ) ")"$ Put (Item => Start, Fore => 1, Aft => 6, Exp => 0 ) Float_Io (Long_Float ) įunction F (X : Long_Float ) return Long_Float is 62.1 Imperative version (Ugly, side effects)Īda with Ada.46.5 Factorization to quadratic factors.