Eigenvalue Determination Task

An Eigenvalue Determination Task is a Numerical Analysis Task that requires eigenvalues for a matrix.

• Context:
  • It can be solved by an Eigenvalue System (that implements an eigenvalue algorithm).
• Example(s):
  • a QR Task.
  • a Quadratic Eigenvalue Task.
  • [math]\displaystyle{ \operatorname{Eigenvalues} \Bigl(\begin{bmatrix} 5 & 4 \\ 1 & 2 \end{bmatrix} \Bigr) = \{6,1\} }[/math].
  • [math]\displaystyle{ \operatorname{Eigenvalues} \Bigl(\begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \Bigr) = \{ 1+2i , 1-2i \} }[/math].
  • [math]\displaystyle{ \operatorname{Eigenvalues} \Bigl(\begin{bmatrix} -2 & 2 & 3 \\ 2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\Bigr) = \{ 5, -3 , -3 \} }[/math] .
• See: Eigenvalue Approximation, Eigenvectors, Numerical Stability, Linear Programming Task.

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References

• http://scholar.google.com/scholar?q="Eigenvalue+determination"
• http://planetmath.org/encyclopedia/EigenvalueProblem.html
• http://en.wikipedia.org/wiki/Quadratic_eigenvalue_problem

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/eigenvalue_algorithm Retrieved:2015-3-3.
  • In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors.

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