General Linear System: Difference between revisions
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== Space | == Time-Space Tradeoff == | ||
[[File:Linear System - General Linear System - Pareto Frontier.png|1000px]] | [[File:Linear System - General Linear System - Pareto Frontier.png|1000px]] | ||
Revision as of 14:41, 15 February 2023
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
