Foundations of Computational Mathematics

Table of Contents

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   Book Overview
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   Chapter 1 Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract)
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   Chapter 2 Essentially Smooth Lipschitz Functions: Compositions and Chain Rules
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   Chapter 3 Junction Detection and Filtering
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   Chapter 4 Recognition in Hierarchical Models
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   Chapter 5 Continuity ∑—Algebras (E xtended A bstract )
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   Chapter 6 Condition Number Analysis for Sparse Polynomial Systems
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   Chapter 7 Residues in the Torus and Toric Varieties
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   Chapter 8 Piecewise Smooth Orthonormal Factors for Fundamental Solution Matrices
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    Chapter 9 Algorithms for computing finite semigroups
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    Chapter 10 Extended Grzegorczyk Hierarchy in the BSS Model of Computability
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    Chapter 11 Affine-Invariant Symmetry Sets
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    Chapter 12 On the Qualitative Properties of Modified Equations
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    Chapter 13 Numerical Methods on (and off) Manifolds
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    Chapter 14 On One Computational Scheme Solving the Nonstationary Schrödinger Equation with Polynomial Nonlinearity
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    Chapter 15 Newton Iteration Towards a Cluster of Polynomial Zeros
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    Chapter 16 Szemerédi’s Regularity Lemma for Sparse Graphs
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    Chapter 17 Questions on Attractors of 3-Manifolds
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    Chapter 18 A Trust-Region SLCP Model Algorithm for Nonlinear Programming
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    Chapter 19 On the height used by additives BSS machines
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    Chapter 20 The Space Complexity of Elimination Theory: Upper Bounds
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    Chapter 21 Global Stochastic Recursive Algorithms
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    Chapter 22 Dynamical Recognizers: Real-time Language Recognition by Analog Computers (Extended Abstract)
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    Chapter 23 Solving special polynomial systems by using structured matrices and algebraic residues
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    Chapter 24 Numerical Integration of Differential Equations on Homogeneous Manifolds
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    Chapter 25 A Convergence proof of an Iterative Subspace Method for Eigenvalues Problems
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    Chapter 26 Regularity of Minimizers of the Mumford-Shah Functional
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    Chapter 27 Tests and Constructions of Irreducible Polynomials over Finite Fields
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    Chapter 28 Numerical Linear Algebra in Optical Imaging
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    Chapter 29 Explicit symplectic integration of rod dynamics
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    Chapter 30 Toric Laminations, Sparse Generalized Characteristic Polynomials, and a Refinement of Hubert’s Tenth Problem
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    Chapter 31 Finite-Dimensional Feedback Control of a Scalar Reaction-Diffusion Equation via Inertial Manifold Theory
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    Chapter 32 Computational aspects of jacobian matrices
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    Chapter 33 Rigid body dynamics and measure differential inclusions
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    Chapter 34 Linear decision lists and partitioning algorithms for the construction of neural networks
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    Chapter 35 Ill-Posedness and Finite Precision Arithmetic: A Complexity Analysis for Interior Point Methods
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    Chapter 36 Iterated Commutators, Lie’s Reduction Method and Ordinary Differential Equations on Matrix Lie Groups