Abstract
TheSRSRalgorithm is a structure-preserving algorithm for computing the spectrum of symplectic matrices. Any symplectic matrix can be reduced to symplectic butterfly form. A symplectic matrixBBin butterfly form is uniquely determined by4n−14n-1parameters. Using these4n−14n-1parameters, we show how one step of the symplecticSRSRalgorithm forBBcan be carried out inO(n)\mathcal {O}(n)arithmetic operations compared toO(n3)\mathcal {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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