# Questions tagged [numerical-analysis]

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### How to solve the following problem by using Gaussian elimination with partial pivoting (A=PLU)?

****The Question is here***** (in the link) Given a nonsingular matrix A $\in$ $R^*(nxn)$, how would you solve the following problems efficiently using Gaussian elimination with partial pivoting (the ...
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If bilinear interpolation is faster (uses 4 data points) but less accurate than bicubic interpolation, which uses 16 data points, why is there no "bi-quadratic" interpolation, which would use 9 data ...
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### Are there practical usage of determinants in numerical simulation?

I know the historical importance of the link between linear systems and determinants. I also know that determinants have a beautiful connection with non-singular matrices, i.e., if a matrix is non-...
17 views

### Numerical integration of a function

For a particular physical system, the force is given by $$F(r)=-\frac{d\Phi(r)}{dr}=\frac{r^5+2ar^3+a^2r-4a}{r^4(r^3+ar+2a)}$$ where $\Phi(r)$ is the potential energy which can be obtained as the ...
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935 views

### Difference between order of convergence and order of consistency?

I understand that, as the time step is reduced: Consistency: The local error must approach zero. Convergence: The global error must approach zero. But why are both the order of convergence and ...
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Is there any other options of calculating integral instead of using quadratures? I know that also we can calculate spline function or use monte-carlo method but do you know something else?
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### Why are transcendental functions of large numbers inaccurate on computers?

For instance, why is it hard to accurately compute sin(1e99)? I suspect it has something to do with rounding error.
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### Converge to unknown number with oracle

I'm playing a game where I'm trying to estimate an unknown real number $x$. An oracle exists that will answer the question of "Is a number $y$ greater than or equal to $x$?", to which the oracle will ...
378 views

### Most stable algorithm to solve a system of linear equations?

I am doing some image processing involving solving a system of linear equations. I am getting some errors and bits of the image looks corrupted. I would like to know what is the most stable way to ...
108 views

### “Compressing” rationals given error bounds

I'm working on implementing some exact real arithmetic operations for fun. I've got the rough outline of how I want to do things as well and have figured out how to write most of the important ...