The Impact of Panel Factorization on the Gauss-Huard Algorithm for the Solution of Linear Systems on Modern Architectures

2016 ◽  
pp. 405-416
Author(s):  
Sandra Catalán ◽  
Pablo Ezzatti ◽  
Enrique S. Quintana-Ortí ◽  
Alfredo Remón
Keyword(s):  
Linear Systems ◽  
The Impact

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

scholarly journals A State Optimization Model Based on Kalman Filtering and Robust Estimation Theory for Fusion of Multi-Source Information in Highly Non-linear Systems

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1687 ◽  
Author(s):  
Muhammad Adeel Akram ◽  
Peilin Liu ◽  
Muhammad Owais Tahir ◽  
Waqas Ali ◽  
Yuze Wang
Keyword(s):  
State Estimation ◽  
Linear Systems ◽  
Kalman Filtering ◽  
Information Fusion ◽  
Estimation Theory ◽  
Source Information ◽  
Estimation Model ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Impact

Consistent state estimation is a vital requirement in numerous real life applications from localization to multi-source information fusion. The Kalman filter and its variants have been successfully used for solving state estimation problems. Kalman filtering-based estimators are dependent upon system model assumptions. A deviation from defined assumptions may lead to divergence or failure of the system. In this work, we propose a Kalman filtering-based robust state estimation model using statistical estimation theory. Its primary intention is for multiple source information fusion, although it is applicable to most non-linear systems. First, we propose a robust state prediction model to maintain state constancy over time. Secondly, we derive an error covariance estimation model to accept deviations in the system error assumptions. Afterward, an optimal state is attained in an iterative process using system observations. A modified robust MM estimation model is executed within every iteration to minimize the impact of outlying observation and approximation errors by reducing their weights. For systems having a large number of observations, a subsampling process is introduced to intensify the optimized solution redundancy. Performance is evaluated for numerical simulation and real multi sensor data. Results show high precision and robustness of proposed scheme in state estimation.

scholarly journals Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems

2021 ◽  
Vol 47 (2) ◽  
pp. 1-30
Author(s):  
Hussam Al Daas ◽  
Laura Grigori ◽  
Pascal Hénon ◽  
Philippe Ricoux
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Real Life ◽  
Krylov Subspace Methods ◽  
Krylov Subspaces ◽  
Systems Of Equations ◽  
The Matrix ◽  
Value Decomposition ◽  
The Impact ◽  
Linear Systems Of Equations

This article presents deflation strategies related to recycling Krylov subspace methods for solving one or a sequence of linear systems of equations. Besides well-known strategies of deflation, Ritz-, and harmonic Ritz-based deflation, we introduce an Singular Value Decomposition based deflation technique. We consider the recycling in two contexts: recycling the Krylov subspace between the restart cycles and recycling a deflation subspace when the matrix changes in a sequence of linear systems. Numerical experiments on real-life reservoir simulation demonstrate the impact of our proposed strategy.

scholarly journals Assessing the impact of the CPU power-saving modes on the task-parallel solution of sparse linear systems

2014 ◽  
Vol 17 (4) ◽  
pp. 1335-1348 ◽  
Author(s):  
José I. Aliaga ◽  
María Barreda ◽  
Manuel F. Dolz ◽  
Alberto F. Martín ◽  
Rafael Mayo ◽  
...  
Keyword(s):  
Linear Systems ◽  
Power Saving ◽  
Sparse Linear Systems ◽  
Parallel Solution ◽  
Task Parallel ◽  
The Impact

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

Organic Syntheses During the Impact of a Comet with a Gaseous Planet

1997 ◽  
Vol 161 ◽  
pp. 189-195
Author(s):  
Cesare Guaita ◽  
Roberto Crippa ◽  
Federico Manzini
Keyword(s):  
Polymeric Material ◽  
Molecular Form ◽  
Parent Compound ◽  
Blue Filter ◽  
Organic Syntheses ◽  
The Impact

AbstractA large amount of CO has been detected above many SL9/Jupiter impacts. This gas was never detected before the collision. So, in our opinion, CO was released from a parent compound during the collision. We identify this compound as POM (polyoxymethylene), a formaldehyde (HCHO) polymer that, when suddenly heated, reformes monomeric HCHO. At temperatures higher than 1200°K HCHO cannot exist in molecular form and the most probable result of its decomposition is the formation of CO. At lower temperatures, HCHO can react with NH3 and/or HCN to form high UV-absorbing polymeric material. In our opinion, this kind of material has also to be taken in to account to explain the complex evolution of some SL9 impacts that we observed in CCD images taken with a blue filter.

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