Positive Definite, Hermitian Matrix (Linear System)
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Description
In this case, we restrict $A$ to be positive definite and hermitian (or symmetric, if $A$ is real-valued).
Related Problems
Generalizations: General Linear System
Related: Sparse Linear System, 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 | |
| Cholesky | 1940 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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