Vandermonde Matrix (Linear System)

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Revision as of 10:18, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Vandermonde Matrix (Linear System)}} == Description == In this case, we restrict $A$ to be a Vandermonde matrix. == Related Problems == Generalizations: General Linear System Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix == Parameters == <pre>n: number of variables and number of equations m: number of nonzero entries in matrix k: ratio between largest and sma...")
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Description

In this case, we restrict $A$ to be a Vandermonde matrix.

Related Problems

Generalizations: General Linear System

Related: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz 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
Bjorck-Pereyra 1970 $O(n^{2})$ $O(n^{2})$ total Exact Deterministic Time

Time Complexity graph

Linear System - Vandermonde Matrix - Time.png

Space Complexity graph

Linear System - Vandermonde Matrix - Space.png

Pareto Decades graph

Linear System - Vandermonde Matrix - Pareto Frontier.png