Inexact geometry.

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry

Let {f1, f2, . . . , ft} ⊂ Q[z1, . . . , zN ] be a set of homogeneous polynomials. Let Z denote the complex, projective, algebraic set determined by the homogeneous ideal I = (f1, f2, . . . , ft) ⊂ C[z1, . . . , zN ]. Numerical continuation-based methods can be used to produce arbitrary precision numerical approximations of generic points on each irreducible component of Z. Consider the prime d...

Fourier Analysis of Parallel Inexact Block-Jacobi Splitting with Transport Synthetic Acceleration in Slab Geometry

A Fourier analysis is conducted for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. Both “traditional” TSA (TTSA) and a “modified” TSA (MTSA), in which only the scattering in the low o...

The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances

The Distance Geometry Problem in three dimensions consists in finding an embedding in R of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem that can be discretized under some assumptions on the minimum degree of the vertices. In this paper we discuss the case whe...

The Branch and Prune Algorithm for the Molecular Distance Geometry Problem with Inexact Distances

The Discretizable Molecular Distance Geometry Problem (DMDGP) consists in a subclass of distance geometry instances (related to molecules) that can be solved by combinatorial optimization. A modified version of the Branch and Prune (BP) algorithm, previously proposed for solving these instances, is presented, where it is supposed that exact distances are not known, but rather intervals where th...

Accelerated Inexact Newton