Huge Linear equation system

Question

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.

Answer 1

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

Answer 2

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.

Answer 3

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 $x_1<x_2<\ldots<x_n$.

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 $k=1,\ldots,n+1$.