Error Analysis for Iterative Methods
In this section we investigate the order of convergence of functional iteration schemes and, as a means of obtaining ra…
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Mathematical Preliminaries and Error Analysis Part 2
Review Of Calculus The integral is the other basic concept of calculus that is used extensively.The Riemann int…
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The Method of False Position
Each successive pair of approximations in the Bisection method brackets a root $p$ of the equation; that is, for each p…
The Secant Method
Newton’s method is an extremely powerful technique, but it has a major weakness: the need to know the value of the der…
Newton`s Method and Its Extensions
If we only want an algorithm, we can consider the technique graphically, as is often done in calculus. Another possibil…
Bisection Methods Aplication
The equation $f(x)=x^3+4x^2-10=0$ has a root in $[1,2]$ since $f(1)=-5$ and $f(2)=14$. It is easily seen from a sketch…
Solutions of Equations of One Variable With The Bisection Method
In this chapter we consider one of the most basic problems of numerical approximation, the root finding problem. This…