![]() In this method we are given a function f(x) and we approximate 2 roots a and b for the function such that f(a).f(b) # include double F ( double x ) /*A sample run of the program was carried out and the results were found as:- This program illustrates the bisection method in C x^3 + 3*x - 5 = 0 Enter the first approximation to the root 1 Enter the second approximation to the root 2 Enter the number of iterations you want to perform 9 The root after 1 iteration is 1.500000 The root after 2 iteration is 1.250000 The root after 3 iteration is 1.125000 The root after 4 iteration is 1.187500 The root after 5 iteration is 1.156250 The root after 6 iteration is 1.146025 The root after 7 iteration is 1.148438 The root after 8 iteration is 1.152344 The root after 9 iteration is 1.154297 The root is 1. ![]() This technique is based on the Intermediate Value Theorem which states that if f(x) f ( x) is a continuous function in a,b a, b and if q q is any number between f(a) f ( a) and f(b) f ( b) ,then, there exists a number c c in (a,b) ( a, b) such that f(q) c f ( q) c. Bisection method is one of the many root finding methods. Bisection method is a technique to find the roots of algebraic and transcendental equations of the form f(x) 0 f ( x) 0 such as: xex 1 0 x e x - 1 0. a) If f (x L )f (x M) < 0, the graph of the function crosses the x-axis somewhere between x L and x M, so the. x U - Upper (right) endpoint of an interval. x L - Lower (left) endpoint of an interval. *This program in C is used to demonstarte bisection method. I'm not convinced that you understand what the above means. IMSL Fortran Library User's Guide MATH / LIBRARY Volume 1 of 2 Mathematical Functions in Fortran IMSL, PV-WAVE, and VISUAL NUMERICS are registered in the U.S. ![]()
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