The parameterized \(SR\) algorithm for symplectic (butterfly) matrices (Q2723526)
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scientific article; zbMATH DE number 1614796
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The parameterized \(SR\) algorithm for symplectic (butterfly) matrices |
scientific article; zbMATH DE number 1614796 |
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5 July 2001
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symplectic matrix
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eigenvalue problem
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\(SR\) algorithm
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butterfly matrix
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The parameterized \(SR\) algorithm for symplectic (butterfly) matrices (English)
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The \(SR\) algorithm is a structure-preserving algorithm for computing the spectrum of symplectic matrices. Any symplectic matrix can be reduced to symplectic butterfly form. A symplectic matrix \(B\) in butterfly form is uniquely determined by \(4n-1\) parameters. Using these \(4n-1\) parameters is shown, how one step of the symplectic \(SR\) algorithm for \(B\) can be carried out in \(O(n)\) arithmetic operation compared to \(O(n^3)\) arithmetic operations when working on the actual symplectic matrix. Moreover, the symplectic structure, which will be destroyed in the numerical process due to roundoff errors when working with a symplectic (butterfly) matrix, will be forced by working just with the parameters.
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