The projected gradient methods for least squares matrix approximations with spectral constraints
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Unitary integrators and applications to continuous orthonormalization techniques
SIAM Journal on Numerical Analysis
Dynamical Systems that Compute Balanced Realizations and the Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Computation of a few Lyapunov exponents for continuous and discrete dynamical systems
Applied Numerical Mathematics - Special issue on numerical methods for ordinary differential equations
Numerical solution of isospectral flows
Mathematics of Computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Newton-type methods for solving nonlinear equations on quadratic matrix groups
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
Approximating the exponential from a Lie algebra to a Lie group
Mathematics of Computation
Applied Numerical Mathematics
Generalized Polar Decompositions for the Approximation of the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
Geometric Integration on Manifold of Square Oblique Rotation Matrices
SIAM Journal on Matrix Analysis and Applications
A Class of Intrinsic Schemes for Orthogonal Integration
SIAM Journal on Numerical Analysis
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Exponential monotonicity of quadratic forms in ODEs and preserving methods
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Smooth SVD on the Lorentz group with application to computation of Lyapunov exponents
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
On the Low-Rank Approximation of Data on the Unit Sphere
SIAM Journal on Matrix Analysis and Applications
Computation of the Exponential of Large Sparse Skew-Symmetric Matrices
SIAM Journal on Scientific Computing
Analysis of Projection Methods for Rational Function Approximation to the Matrix Exponential
SIAM Journal on Numerical Analysis
Hi-index | 7.29 |
In recent years differential systems whose solutions evolve on manifolds of matrices have acquired a certain relevance in numerical analysis. A classical example of such a differential system is the well-known Toda flow. This paper is a partial survey of numerical methods recently proposed for approximating the solutions of ordinary differential systems evolving on matrix manifolds. In particular, some results recently obtained by the author jointly with his co-workers will be presented. We will discuss numerical techniques for isospectral and isodynamical flows where the eigenvalues of the solutions are preserved during the evolution and numerical methods for ODEs on the orthogonal group or evolving on a more general quadratic group, like the symplectic or Lorentz group. We mention some results for systems evolving on the Stiefel manifold and also review results for the numerical solution of ODEs evolving on the general linear group of matrices.