Polynomial regression: Difference between revisions

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In [[linear algebra]], '''Wilkinson matrices''' are [[Symmetric matrix|symmetric]], [[Tridiagonal matrix|tridiagonal]], order-''N'' [[matrix (math)|matrices]] with pairs of nearly, but not exactly, equal [[eigenvalue]]s.<ref>{{cite book | title = The Algebraic Eigenvalue Problem | author = Wilkinson | edition = | publisher = [[Oxford University Press]] | year = 1965 | isbn = 0-19-853418-3}}</ref> It is named after the British mathematician [[James H. Wilkinson]]. For ''N''&nbsp;=&nbsp;7, the Wilkinson matrix is given by
 
:<math>\begin{bmatrix}
3 & 1 & 0 & 0 & 0 & 0 & 0 \\
1 & 2 & 1 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & 1 & 2 & 1 \\
0 & 0 & 0 & 0 & 0 & 1 & 3 \\
\end{bmatrix}.</math>
 
Wilkinson matrices have applications in many fields, including [[scientific computing]], [[numerical linear algebra]], and [[signal processing]].
 
==References==
{{reflist}}
 
{{Numerical linear algebra}}
 
[[Category:Matrices]]
[[Category:Numerical linear algebra]]
 
 
{{Linear-algebra-stub}}

Revision as of 19:09, 28 January 2014

In linear algebra, Wilkinson matrices are symmetric, tridiagonal, order-N matrices with pairs of nearly, but not exactly, equal eigenvalues.[1] It is named after the British mathematician James H. Wilkinson. For N = 7, the Wilkinson matrix is given by

[3100000121000001110000010100000111000001210000013].

Wilkinson matrices have applications in many fields, including scientific computing, numerical linear algebra, and signal processing.

References

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Template:Numerical linear algebra


Template:Linear-algebra-stub

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