Newton-type methods for solving nonlinear equations on quadratic matrix groups

DOI10.1016/S0377-0427(99)00184-3zbMath0947.65058MaRDI QIDQ1971839

C. Mastroserio, Luciano Lopez, Tiziano Politi

Publication date: 7 June 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceNewton's methodnonlinear systemsnonlinear matrix equationquadratic matrix groups

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Matrix equations and identities (15A24) Analysis on real and complex Lie groups (22E30)

Related Items (3)

Improved Newton iteration for nonlinear matrix equations on quadratic Lie groups ⋮ Exact low-order polynomial expressions to compute the Kolmogoroff–Nagumo mean in the affine symplectic group of optical transference matrices ⋮ Numerical methods for ordinary differential equations on matrix manifolds

Cites Work

• Applications of Newton's method to some numerical problems in matrix theory
• The Cayley transform in the numerical solution of unitary differential systems
• Modeling and solution of some mechanical problems on Lie groups
• Numerical integration of ordinary differential equations on manifolds
• Runge-Kutta methods on Lie groups
• The Newton iteration on Lie groups
• Matrix factorizations for symplectic QR-like methods
• On the solution of linear differential equations in Lie groups
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• Unitary Integrators and Applications to Continuous Orthonormalization Techniques

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