Foundations of Computational Mathematics, Volume 8

Volume 8, Number 1, February 2008

Carlos Beltrán, Luis Miguel Pardo:
On Smale's 17th Problem: A Probabilistic Positive Solution. 1-43
Saugata Basu:
Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time. 45-80
Saugata Basu:
Errata for Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time. 81-95
Saugata Basu, Richard Pollack, Marie-Françoise Roy:
Computing the First Betti Number of a Semi-Algebraic Set. 97-136
Hendrik Hubrechts:
Point Counting in Families of Hyperelliptic Curves. 137-169

Andrew J. Sommese, Charles W. Wampler:
Exceptional Sets and Fiber Products. 171-196
Felipe Alvarez, Jérôme Bolte, Julien Munier:
A Unifying Local Convergence Result for Newton's Method in Riemannian Manifolds. 197-226
Hans Z. Munthe-Kaas, Will M. Wright:
On the Hopf Algebraic Structure of Lie Group Integrators. 227-257
Alan Edelman, Brian D. Sutton:
The Beta-Jacobi Matrix Model, the CS Decomposition, and Generalized Singular Value Problems. 259-285

Per Christian Moan, Jitse Niesen:
Convergence of the Magnus Series. 291-301
Elena Celledoni, David Cohen, Brynjulf Owren:
Symmetric Exponential Integrators with an Application to the Cubic Schrödinger Equation. 303-317
Ernst Hairer, Christian Lubich:
Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times. 319-334
Robert I. McLachlan, Hans Z. Munthe-Kaas, G. R. W. Quispel, Antonella Zanna:
Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields. 335-355
Sergio Blanes, Fernando Casas, Ander Murua:
On the Linear Stability of Splitting Methods. 357-393
B. J. C. Baxter:
On Spherical Averages of Radial Basis Functions. 395-407

Nira Dyn, Armin Iske, Holger Wendland:
Meshfree Thinning of 3D Point Clouds. 409-425
Elizabeth L. Mansfield, Peter E. Hydon:
Difference Forms. 427-467
Anthony M. Bloch, Peter E. Crouch, Jerrold E. Marsden, Amit K. Sanyal:
Optimal Control and Geodesics on Quadratic Matrix Lie Groups. 469-500
Jeongoo Cheh, Peter J. Olver, Juha Pohjanpelto:
Algorithms for Differential Invariants of Symmetry Groups of Differential Equations. 501-532

Yurii Nesterov, A. Nemirovski:
Primal Central Paths and Riemannian Distances for Convex Sets. 533-560
Yiming Ying, Massimiliano Pontil:
Online Gradient Descent Learning Algorithms. 561-596
Daqing Wan:
Modular Counting of Rational Points over Finite Fields. 597-605
Jean B. Lasserre, Monique Laurent, Philipp Rostalski:
Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals. 607-647

N. Raj Rao, Alan Edelman:
The Polynomial Method for Random Matrices. 649-702
Stephen J. Dilworth, E. Odell, T. Schlumprecht, A. Zsák:
Coefficient Quantization in Banach Spaces. 703-736
Stefan Kunis, Holger Rauhut:
Random Sampling of Sparse Trigonometric Polynomials, II. Orthogonal Matching Pursuit versus Basis Pursuit. 737-763
J. Maurice Rojas:
Book Review S. Basu, R. Pollack, and M.-F. Roy: Algorithms in Real Algebraic Geometry. 765-771