# Tagged Questions

A linearly independent set of elements of a vector space such that any element in that vector space can be expressed as a linear combination of the elements of the basis.

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### Computing size of N-Dimensional Polynomial Basis and Efficient Representation of Basis

A problem I have had on my mind recently has been a compact way to compute the size of an $N$-Dimensional Polynomial basis of some order $p$, where a linear basis is $p=1$. I have attempted searching ...
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### Choice of basis in FEM

Briefly, what are the different types of basis used in FEM and why is the nodal basis so popular and advantageous in the finite element context?
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### Using SVD to biorthogonalize left and right eigenvectors?

I have a set of left and right eigenvectors from an nonsymmetric eigenproblem, and I'd like to biorthogonalize them. I tried Gram-Schmidt, but this fails for most cases. I then read that the SVD is ...
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### Which libraries have good implementations of Basis splines?

I'm looking to use the finite element method with B-splines as my function basis. Which C/C++ libraries have good B-spline support? Specifically, I'm looking for an implementation of a stable ...
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### How to do FEM in sector elements?

Suppose we have an element in the polar coordinate as $0\leq r\leq 1$, $0\leq\theta\leq \alpha$. What are the correct basis functions in this element? For this kind of mesh, there are a lot of ...
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### Polynomials that are orthogonal over curves in the complex plane

Various important sets of polynomials (Legendre, Chebyshev, etc.) are orthogonal over some real interval with some weighting. Are there known families of polynomials that are orthogonal over other ...
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### Differences between Gaussian and Slater functions on the quality of the results?

Given two computational programs, one using a Gaussian basis, and the other using Slater basis, what are the practical differences, advantages and disadvantages for each choice ?
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### What does it mean for a basis set to be “correlation consistent” ?

Some basis sets are said to be "correlation consistent". What does it mean in practice ?