1
$\begingroup$

Do you know any repository of huge matrices of a linear system?, Or to tell a problem in which a lot of linear equations are needed?

I want to solve huge linear equations systems but have not had any luck when trying to find huge matrices.

  • 0
    In numerical methods for solving partial differential equations - eg finite elements, finite differences, etc - you end out with arbitrarily large matrices as you make the mesh finer and finer.2012-04-24

3 Answers 3

4

You might try http://math.nist.gov/MatrixMarket/

  • 0
    ...and the [links to other sites](http://math.nist.gov/MatrixMarket/links.html) show other places to get nice examples!2012-04-23
2

Let $n\geq 1$ be an integer, and fix $n+1$ points in $\mathbb{R}^2$, say $(x_1,y_1)$, ... , $(x_n,y_n)$, $(x_{n+1},y_{n+1})$, such that x_1.

Problem: find the coefficients of the unique polynomial $p(x)\in \mathbb{R}[x]$ of degree $n$ that interpolates all $n+1$ points, i.e., find coefficients $a_0,\ldots,a_n\in\mathbb{R}$ such that the polynomial $p(x)=a_0+a_1x+\cdots+a_nx^n$ satisfies $p(x_k)=y_k$ for all $k=1,\ldots,n+1$.

  • 0
    Oops, I just noticed that J.D. pointed this one out in a comment.2012-04-24
1

Vast systems of linear equations are solved as part of some integer factorization algorithms, such as the Quadratic Sieve, and the Number Field Sieves (both special and general). Much literature can be found by searching on those terms.