Sparse Linear System (Linear System)
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Description
In this case, we restrict $A$ to be sparse (i.e. $A$ only has $O(n)$ nonzero entries).
Related Problems
Generalizations: General Linear System
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 |
|---|---|---|---|---|---|---|
| Harrow (Quantum) | 2009 | $O(k^{2}*\log n)$ | $O(\log n)$ | Exact | Quantum | Time & Space |