General Linear System (Linear System)

Description

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables. This is typically written in the form $Ax=b$ where $A$ is a matrix and $x, b$ are vectors. In this case, we impose no restrictions on $A$.

Related Problems

Subproblem: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix

Related: Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix

Parameters

$n$: number of variables and number of equations

$m$: number of nonzero entries in matrix

$k$: ratio between largest and smallest eigenvalues

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Gaussian-Jordan Elimination	-150	$O(n^{3})$	$O(n^{2})$	Exact	Deterministic

Time Complexity Graph

Space Complexity Graph

Time-Space Tradeoff