Optimization and dynamical systems (Q1917979)

In this book, dynamical systems in the form of gradient flows on Riemannian manifolds are used to solve problems from linear algebra and linear systems theory. Numerical algorithms performed on matrices are viewed as dynamical systems acting on manifolds of matrices and with Riccati-like behavior. The book intended for engineers and mathematicians alike gives important insight into this rapidly evolving area. The chapter headings are 1. Matrix eigenvalue problems, 2. Double bracket isospectral flows, 3. Singular value decomposition, 4. Linear programming, 5. Approximation and control, 6. Balanced matrix factorizations, 7. Invariant theory and system balancing, 8. Balancing via gradient flows, 9. Sensitivity optimization. The book is concluded by three appendices collecting facts from linear algebra, dynamical systems, and global analysis.