Approximate multi-matroid intersection via iterative refinement

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

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A new iterative refinement of the solution of ill-conditioned linear system of equations

International Journal of Computer Mathematics ◽

10.1080/00207161003713907 ◽

2011 ◽

Vol 88 (5) ◽

pp. 950-956 ◽

Cited By ~ 3

Author(s):

Davod Khojasteh Salkuyeh ◽

Atefeh Fahim

Keyword(s):

Linear System ◽

Iterative Refinement ◽

System Of Equations ◽

Linear System Of Equations

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The VEOS Project

Presence Teleoperators & Virtual Environments ◽

10.1162/pres.1994.3.2.111 ◽

1994 ◽

Vol 3 (2) ◽

pp. 111-129 ◽

Cited By ~ 18

Author(s):

William Bricken ◽

Geoffrey Coco

Keyword(s):

Rapid Prototyping ◽

Virtual Environments ◽

Virtual Environment ◽

Object Oriented ◽

Organization Structure ◽

Object Oriented Programming ◽

Iterative Refinement ◽

Software Infrastructure ◽

Human Interface ◽

Heterogeneous Distributed Computing

The Virtual Environment Operating Shell (veos) was developed at University of Washington's Human Interface Technology Laboratory as software infrastructure for the lab's research in virtual environments. veos was designed from scratch to provide a comprehensive and unified management facility to support generation of, interaction with, and maintenance of virtual environments. VEOS emphasizes rapid prototyping, heterogeneous distributed computing, and portability. We discuss the design, philosophy and implementation of veos in depth. Within the Kernel, the shared database transformations are pattern-directed, communications are asynchronous, and the programmer's interface is LISP. An entity-based metaphor extends object-oriented programming to systems-oriented programming. Entities provide first-class environments and biological programming constructs such as perceive, react, and persist. The organization, structure, and programming of entities are discussed in detail. The article concludes with a description of the applications that have contributed to the iterative refinement of the VEOS software.

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Linear iterative refinement method for the rapid simulation of borehole nuclear measurements: Part I — Vertical wells

Geophysics ◽

10.1190/1.3267877 ◽

2010 ◽

Vol 75 (1) ◽

pp. E9-E29 ◽

Cited By ~ 31

Author(s):

Alberto Mendoza ◽

Carlos Torres-Verdín ◽

Bill Preeg

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Numerical Technique ◽

Integral Form ◽

Computer Time ◽

Iterative Refinement ◽

Detector Response ◽

Layer By Layer ◽

Response Factors ◽

Refinement Method

As a result of its high numerical accuracy and versatility to include complex tool configurations and arbitrary spatial distributions of material properties, the Monte Carlo method is the foremost numerical technique used to simulate borehole nuclear measurements. Although recent advances in computer technology have considerably reduced the computer time required by Monte Carlo simulations of borehole nuclear measurements, the efficiency of the method is still not sufficient for estimation of layer-by-layer properties or combined quantitative interpretation with other borehole measurements. We develop and successfully test a new linear iterative refinement method to simulate nuclear borehole measurements accurately and rapidly. The approximation stems from Monte Carlo-derived geometric response factors, referred to as flux sensitivity functions (FSFs), for specific density and neutron-tool configurations. Our procedure first invokes the integral representation of Boltzmann’s transport equation to describe the detector response from the flux of particles emitted by the radioactive source. Subsequently, we use theMonte Carlo N-particle (MCNP) code to calculate the associated detector response function and the particle flux included in the integral form of Boltzmann’s equation. The linear iterative refinement method accounts for variations of the response functions attributable to local perturbations when numerically simulating neutron and density porosity logs. We quantify variations in the FSFs of neutron and density measurements from borehole environmental effects and spatial variations of formation properties. Simulations performed with the new approximations yield errors in the simulated value of density of less than [Formula: see text] with respect to Monte Carlo-simulated logs. Moreover, for the case of radial geometric factor of density, we observe a maximum shift of [Formula: see text] at 90% of the total sensitivity as a result of realistic variations of formation density. For radial variation of neutron properties (migration length), the maximum change in the radial length of investigation is [Formula: see text]. Neutron porosity values simulated with the new approximation differ by less than 10% from Monte Carlo simulations. The approximations enable the simulation of borehole nuclear measurements in seconds of CPU time compared to several hours with MCNP.

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