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## Bisection Method – Algorithm, Flowchart and Code in C

Bisection Method Illustration

The *bisection method* is one of the simplest and most reliable of iterative methods for the solution of nonlinear equations. This method, also known as *binary chopping* or *half-interval* method, relies on the fact that if *f(x)* is real and continuous in the interval *a < x < b*, and *f(a)* and *f(b)* are of opposite signs, that is,

*f(a)*f(b) < 0*

then there is at least one real root in the interval between a and b.

## C Program implementing Lagrange Interpolation Formula

In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points **Xi** and numbers **Yi**, the Lagrange polynomial is the polynomial of the least degree that at each point **Xj** assumes the corresponding value **Yj** (i.e. the functions coincide at each point). The interpolating polynomial of the least degree is unique, however, and it is therefore more appropriate to speak of “the Lagrange form” of that unique polynomial rather than “the Lagrange interpolation polynomial”, since the same polynomial can be arrived at through multiple methods.

The Lagrange interpolating polynomial is the polynomial **P(X)** of degree * <=(n – 1)* that passes through the

*points*

**n***, and is given by*

**(x1, y1 = f(x1)),(x2, y2 = f(x2)) ,.., (xn, yn = f(xn)),**