Tagged Questions

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Newton's Method for Roots of Polynomials

The standard way to use Newton's Method for finding a root of a polynomial $p(x)$ is to use the iteration formula $$x_{n+1}=x_n-{p(x)\over p'(x)}$$ I recently thought of a new way of finding the ...
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How to evaluate a condition number for a function of several variables.

I'm trying to get the condition number of a function $f(a,b,c)$ to see if it is stable. It is multivariate. I am reading the information here ...
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Infinite Order Fourier Series and Infinite Series with Piecewise Function

Given $$f(x) = \left\{ \begin{array}{ll} 4\pi^2 & \quad x = 0 \\ x^2 & \quad 0<x\le2\pi \end{array} \right.$$ First, compute the infinite ...
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calculate Jacobian matrix without closed form or analytical form

The question is probably clear in the title. In many of my applications mostly computer vision, I might not have the closed-form or analytical form of f (a multivariable function). It's calculated ...
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Numerical root finding of function with unknown parameters

I have a multivariate function of which I want to find one of (or all) its roots. However, besides the variables, it also depends on a bunch of parameters. Now I only want to find roots which are ...
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How to find an error estimate for integral of curvilinear surface triangle when using quadrature

I would like to find a way to estimate the error due to the calculation of the normal when one tries to find the volume of a volume composed of quadratic surface triangles using numerical gauss ...