Symplectic Methods for the Symplectic Eigenproblem

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Linear Algebra Appl. Benner and H. An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem.

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Bunse-Gerstner and V. A symplectic QR like algorithm for the solution of the real algebraic Riccati equation. IEEE T.

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Runger and M. Kwakernaak and R. Linear Optimal Control Systems. Wiley, Van Loan.

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A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix. Matsuo and T.

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The optimal block-size for the block Gram—Schmidt orthogonalization. On theoretical and numerical aspects of symplectic Gram—Schmidt-like algorithms, Numer. Algorithms —, Salam and E.

Quantum Chemistry 3.3 - Eigenvalues and Eigenfunctions

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Click on the cover image above to read some pages of this book! The solution of eigenvalue problems is an integral part of many scientific computations. For example, the numerical solution of problems in structural dynamics, electrical networks, macro-economics, quantum chemistry, and c- trol theory often requires solving eigenvalue problems.

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The coefficient matrix of the eigenvalue problem may be small to medium sized and dense, or large and sparse containing many zeroelements. In the past tremendous advances have been achieved in the solution methods for symmetric eigenvalue pr- lems. The state of the art for nonsymmetric problems is not so advanced; nonsymmetric eigenvalue problems can be hopelessly difficult to solve in some situations due, for example, to poor conditioning. Good numerical algorithms for nonsymmetric eigenvalue problems also tend to be far more complex than their symmetric counterparts.

This book deals with methods for solving a special nonsymmetric eig- value problem; the symplectic eigenvalue problem. The symplectic eigenvalue problem is helpful, e. Certain quadratic eigenvalue problems arising, e. The problem appears in other applications as well. Country of Publication: US Dimensions cm : Help Centre.


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