aicm swMATH ID: 11487 Software Authors: Marletta, Marco Description: Numerical solution of eigenvalue problems for Hamiltonian systems. The paper concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations with nonlinear dependence on a real eigenparameter λ. Separated boundary conditions are treated. The coefficients are at least continuously differentiable as a function of λ. Using Θ matrices of Atkinson the author constructs an increasing integer-valued function M(λ) whose only points of increase are discontinuities at the eigenvalues, and the size of the discontinuity is equal to the multiplicity of the corresponding eigenvalue. The author describes two alternative approaches to the problem of computing the function M(λ). Some numerical experiments using these algorithms are presented. The author informs that both codes are fully documented and are written in Fortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f. Homepage: http://www.netlib.org/aicm/ Dependencies: netlib Keywords: eigenvalue; Hamiltonian system; nonlinear dependence; numerical experiments Related Software: SLEUTH; SLEIGN2; SLEDGE; LAPACK; Netlib Cited in: 11 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Numerical solution of eigenvalue problems for Hamiltonian systems. Zbl 0833.65083Marletta, Marco 1994 all top 5 Cited by 15 Authors 6 Marletta, Marco 2 Maple, Carsten R. 1 Brown, B. Malcolm 1 Elyseeva, Julia V. 1 Greenberg, Leon 1 Howson, W. Paul 1 Jones, Antonia J. 1 Li, Kun 1 Mirzaei, Hanif 1 Šimon Hilscher, Roman 1 Wang, Yicao 1 Watson, Andrew J. 1 Williams, Frederic W. 1 Zettl, Anton 1 Zhang, Maozhu all top 5 Cited in 8 Serials 2 Journal of Computational and Applied Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Acta Mechanica 1 Journal of Mathematical Analysis and Applications 1 Numerical Algorithms 1 Linear Algebra and its Applications 1 Advances in Computational Mathematics 1 Computational Methods for Differential Equations all top 5 Cited in 7 Fields 9 Ordinary differential equations (34-XX) 6 Numerical analysis (65-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year