# Questions tagged [numerical-methods]

Questions on numerical methods; methods for approximately solving various problems that often do not admit exact solutions. Such problems can be in various fields. Numerical methods provide a way to solve problems quickly and easily compared to analytic solutions.

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### Galerkin Method: Why Set the Residuals to Zero?

I don't understand why the Galerkin method weighs the residual by the shape functions and sets it equal to zero. I'd like to know the reason why. Any intuitive explanation would be greatly appreciated....
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Why sometime our conjugate gradient routine never reaches the stop condition even if the result is correct? As stop condition we use the following: $$\delta > \epsilon^2 \delta_0$$ To avoid ...
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### extension of trigonometric functions as basis functions to higher dimensions

Trigonometric functions forms an orthonormal basis functions for $L^2[a,b]$, with corresponding normalization coefficients. I want to know if this result can be extended to higher dimensions. For ...
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### Best way to fit an equation for the given graph

I have 450 pair $(x,y)$ of data. The plot is like this: I need to fit an equation: $y=f(x)$ for the given data, and to find out values of $y$ when $x=500$. Now, my question is: What kind of ...
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### min/max in front of a sigma sign (Numerical Analysis)

I have an assignment in my Numerical Analysis class that involves an approximation of an integral with a sum. The sum looks to me like a Riemann sum, but I don't know what the "min" in front of the ...
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### Proof of theorem about iterative methods

How do I prove that if $A$ is a tridiagonal (or block tridiagonal) matrix then the corresponding $P_J$ and $P_G$ iteration matrices for the Jacobi and Gauss-Seidel methods satisfy that if $\lambda$ is ...
I'm trying to find a list of IVPs with known solutions to test my implementation of some numerical techniques. The only one I know of is: $$f(x,y)= y' =-\lambda y\;,\;\;\; y(0)=1$$ with the ...
This method could also possibly be applicable to matrices of higher dimension, but for the simplicity of my question i will only ask it for $2$x$2$matrices. Suppose \$A=\begin{pmatrix} a_{11} & a_{...