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 Vogels Approximation Method 

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Here we have an unknown function but we can have every value of function respect to every input. so there I used a fuzzy approximation method I
to approximate the function, here I used sin function to compare answers.
there is a function "isinrange" to find membership values.



%%%%%%%%%%%%%%%%%% EULER_modified_ODE.m %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Euler modified approximation method to solve IVP ODEs
% f defines the function f(t,y)
% t0 defines initial value of t
% y0 defines initial value of y



%%%%%%%%%%%%%%%%% EULER_backward_ODE.m %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Euler modified approximation method to solve IVP ODEs
% f defines the function f(t,y)
% t0 defines initial value of t
% y0 defines initial value of y



% [t, y]=EULER_forward_ODE(f, t0, y0, tend, Niter)
% Euler forward approximation method to solve IVP ODEs
% f defines the function f(t,y)
% t0 defines initial value of t
% y0 defines initial value of y







In the present program three methods are used to solve a heat conduction problem. This problem is given in M. N. doOCozisik, Heat Conduction, Wiley, New York, 1980. We use pdepe, short times solution based on analytical inversion of a Laplace...



Program for global minimization of a concave function.
We implement the algorithm of Harold. P Benson which can be found in the
paper " A Branch and Bound-Outer Approximation Algorithm for Concave Minimization over a Convex...



To further understand the implementation of hyperparameters re-estimation technique in Bayesian hierarchical model, we added two more prior assumptions over the weight in BayesPI, namely Laplace prior and Cauchy prior, by using the evidence...



This code evaluates the root of transcendental equation with the help of Newton Raphson method with enhanced features like vanishing of differential of a function, Infinite cycling for root due to a poor initial approximation or when a root exists...



To calculate an area S(A) of a figure A, bounded by a Jordan curve (which in our case is constructed by a cubic spline
approximation) the Monte Carlo method is applied



Newton's method for solving a system of nonlinear equations, see http://en.wikipedia.org/wiki/Newton's_method

Newton(X,F,X0) solves nonlinear system F(x)=0 by Newton's method, using the given initial approximation X0. The derivative...



MdoDsller's method uses three points, It constructs a parabola through these three points, and takes the intersection of the x-axis with the parabola to be the next approximation. The order of convergence of MdoDsller's method is approximately...



pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 ...

The program performs this computation and prints the approximation after every iteration, so you can see the decimal places converging one by one.

There are three programs, each more...



This method computes an accurate continuous approximation of the DW-MRI signal using adaptive kernels (A. Barmpoutis et al. "Adaptive kernels for multi-fiber reconstruction", In the Proceedings of IPMI, 2009). The approximation is based...



Least Square method is common curve fitting approch. But for special some function, the tradiational Least Square method is hard to get enough accurancy dueo to gobal approximation. Moving Least Square(MLS) can fit any differentiable function...



Least Square method is common curve fitting approch. But for special some function, the tradiational Least Square method is hard to get enough accurancy dueo to gobal approximation. Moving Least Square(MLS) can fit any differentiable function...



This function shows an approximation of the Julia set boundary for the functions of the form P(z) = z^2 + C. The inverse iteration is a method for calculating previous values of z by doing z = sqrt(z-c). By doing this, points along the boundary...



A simple decorator that helps define abstract methods: when such a method is called, an appropriate exception is raised.



This code computes the approximation of the convolution integral (*) between two functions, f(t) and g(t), sampled at the times t1,t2,...,tm (unit spacing), via the trapezoidal quadrature rule. To compute the integral with other than unit spacing,...



Golden section method - searching for minimum of the function on given interval <a,b> files:

golden.m - main algorithm, computing minimum on interval
f.m - given function - file to modify by the user!



This is the fastest (though not most accurate) method of fitting a circlle to data points on a plane (given by their xy-coordinates). It returns the circle center (a,b) and radius R. It was proposed by I. Kasa in article "A curve fitting...