Gregory Newton Backward Interpolation Method can be used to derive difference formula when the x values are at equidistant intervals and the value to be interpolated lies towards the end of the table. Below is a detailed explanation of how to apply Gregory Newton Backward Interpolation Method –
We use various Numerical methods to solve algebraic and transcendental equations. All these methods converge the result to a single root after various approximations specific to each method. In this article we delve into details of rate of convergence of two popular methods – Iterative and Newton Raphson method. Enjoy!
Ok, here is a beautiful mathematical solution to find the Linear Fractional Transformation which maps |Z| <= 1 on to |W| <=1 such that Z = i/4 is mapped onto W=0. Also we will graph out the images of the lines x=c and y=c.
Here is a mathematical solution for forming a Bi-Linear Transformation which maps the points (1, i,-1) onto the points (i,0,-i) and hence finding the image of |Z| < 1 and also finding the Invarient points of this Transformation 🙂
Regular Falsi method is a numerical method to derive the root of a polynomial. The advantage of Regular Falsi over Bisection method is that the convergence is made faster. Below is explanation with a graphical representation and the solution –
Bisection method is the most simplest method of solving algebraic or transcendental equations. It involves selecting an interval [a,b] in which the root lies such that f(a)f(b) < 1. Below is a detailed solved version to find root of x = e<sup>-x</sup>. Enjoy!!
Solving 1.5x – tanx – 0.1 = 0, using iteration method – Iteration is a method of solving algebraic or transcendental equation and is widely used in computer mechanics and programming algorithms. A hand-written solution is as below –
Solving x = 1/ (1+x)1/2 using iteration method – Iteration is a method of solving algebraic or transcendental equation and is widely used in computer mechanics and programming algorithms. A hand-written solution is as below –