Positive Definite, Hermitian Matrix: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Positive Definite, Hermitian Matrix (Linear System)}} == 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 == <pre>n: number of variables and number of equations m: number of nonzero e...") |
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== Parameters == | == Parameters == | ||
n: number of variables and number of equations | |||
m: number of nonzero entries in matrix | m: number of nonzero entries in matrix | ||
k: ratio between largest and smallest eigenvalues | |||
k: ratio between largest and smallest eigenvalues | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Revision as of 13:02, 15 February 2023
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 |
|---|---|---|---|---|---|---|
| Cholesky | 1940 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic |
Time Complexity graph
Space Complexity graph
Pareto Decades graph
