On the Iwasawa decomposition of a symplectic matrix
Copyright policy )On the Iwasawa decomposition of a symplectic matrix
Let \(Sp(n, \mathbb R)=\{S\in SL_{2n}(\mathbb R) : S^tJS=J\}\) be the Lie group of symplectic matrices. The authors present an algorithm for computing the Iwasawa decomposition of a matrix \( Sp(n, \mathbb R)\ni S=KAN\), where \(K\) is compact, \(A\) abelian, and \(N\) nilpotent matrices, via the QR fractorization. The algorithm presented improves the method recently described by \textit{T.-Y. Yam} [Computing Iwasawa decomposition of a symplectic matrix by Cholesky factorization, Appl. Math. Lett. (to appear)], as it is more accurate and efficient.
- Emory University United States
- Scuola Normale Superiore Italy
algorithm, Algebraic systems of matrices, Applied Mathematics, Numerical stability, Other matrix algorithms, QR factorization, Iwasawa decomposition, Factorization of matrices, numerical stability, Symplectic group, Linear algebraic groups over the reals, the complexes, the quaternions, Cholesky factorization; Iwasawa decomposition; Numerical stability; QR factorization; Symplectic group; Applied Mathematics, Hermitian, skew-Hermitian, and related matrices, symplectic group, Cholesky factorization
algorithm, Algebraic systems of matrices, Applied Mathematics, Numerical stability, Other matrix algorithms, QR factorization, Iwasawa decomposition, Factorization of matrices, numerical stability, Symplectic group, Linear algebraic groups over the reals, the complexes, the quaternions, Cholesky factorization; Iwasawa decomposition; Numerical stability; QR factorization; Symplectic group; Applied Mathematics, Hermitian, skew-Hermitian, and related matrices, symplectic group, Cholesky factorization
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).18 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!