Title	Foundations of Computational Mathematics [electronic resource] : Selected Papers of a Conference Held at Rio de Janeiro, January 1997 / edited by Felipe Cucker, Michael Shub
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1997
Connect to	http://dx.doi.org/10.1007/978-3-642-60539-0
Descript	XV, 441 p. 11 illus. online resource

This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics (FoCM) conference at IMPA in Rio de Janeiro in January 1997. FoCM brings together a novel constellation of subjects in which the computational process itself and the foundational mathematical underpinnings of algorithms are the objects of study. The Rio conference was organized around nine workshops: systems of algebraic equations and computational algebraic geometry, homotopy methods and real machines, information based complexity, numerical linear algebra, approximation and PDE's, optimization, differential equations and dynamical systems, relations to computer science and vision and related computational tools. The proceedings of the first FoCM conference will give the reader an idea of the state of the art in this emerging discipline

Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract) -- Essentially Smooth Lipschitz Functions: Compositions and Chain Rules -- Junction Detection and Filtering -- Recognition in Hierarchical Models -- Continuity ?โAlgebras (Extended Abstract) -- Condition Number Analysis for Sparse Polynomial Systems -- Residues in the Torus and Toric Varieties -- Piecewise Smooth Orthonormal Factors for Fundamental Solution Matrices -- Algorithms for computing finite semigroups -- Extended Grzegorczyk Hierarchy in the BSS Model of Computability -- Affine-Invariant Symmetry Sets -- On the Qualitative Properties of Modified Equations -- Numerical Methods on (and off) Manifolds -- On One Computational Scheme Solving the Nonstationary Schrรถdinger Equation with Polynomial Nonlinearity -- Newton Iteration Towards a Cluster of Polynomial Zeros -- Szemerรฉdiโs Regularity Lemma for Sparse Graphs -- Questions on Attractors of 3-Manifolds -- A Trust-Region SLCP Model Algorithm for Nonlinear Programming -- On the height used by additives BSS machines -- The Space Complexity of Elimination Theory: Upper Bounds -- Global Stochastic Recursive Algorithms -- Dynamical Recognizers: Real-time Language Recognition by Analog Computers (Extended Abstract) -- Solving special polynomial systems by using structured matrices and algebraic residues -- Numerical Integration of Differential Equations on Homogeneous Manifolds -- A Convergence proof of an Iterative Subspace Method for Eigenvalues Problems -- Regularity of Minimizers of the Mumford-Shah Functional -- Tests and Constructions of Irreducible Polynomials over Finite Fields -- Numerical Linear Algebra in Optical Imaging -- Explicit symplectic integration of rod dynamics -- Toric Laminations, Sparse Generalized Characteristic Polynomials, and a Refinement of Hilbertโs Tenth Problem -- Finite-Dimensional Feedback Control of a Scalar Reaction-Diffusion Equation via Inertial Manifold Theory -- Computational aspects of jacobian matrices -- Rigid body dynamics and measure differential inclusions -- Linear decision lists and partitioning algorithms for the construction of neural networks -- Ill-Posedness and Finite Precision Arithmetic: A Complexity Analysis for Interior Point Methods -- Iterated Commutators, Lieโs Reduction Method and Ordinary Differential Equations on Matrix Lie Groups

1. Mathematics
2. Algorithms
3. Algebra
4. Mathematical analysis
5. Analysis (Mathematics)
6. Geometry
7. Number theory
8. Topology
9. Mathematics
10. Algebra
11. Number Theory
12. Geometry
13. Algorithm Analysis and Problem Complexity
14. Topology
15. Analysis