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## Análise de erro de funções de pedotransferência na estimativa de retenção de água no solo por meio de árvore de decisão; Error analysis of pedotransfer functions in estimating soil water retention by using decision tree

Raquel Stucchi Boschi
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
65.89%

## Error Analysis of a Partial Pivoting Method for Structured Matrices

Sweet, Douglas R; Brent, Richard P
Tipo: Working/Technical Paper Formato: 322757 bytes; 356 bytes; application/pdf; application/octet-stream
EN_AU
Relevância na Pesquisa
65.86%
Many matrices that arise in the solution of signal processing problems have a special displacement structure. For example, adaptive filtering and direction-of-arrival estimation yield matrices of Toeplitz type. A recent method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian elimination with partial pivoting for such structured matrices. In this paper, a rounding error analysis is performed on the Cauchy and Toeplitz variants of the GKO method. It is shown the error growth depends on the growth in certain auxiliary vectors, the generators, which are computed by the GKO algorithms. It is also shown that in certain circumstances, the growth in the generators can be large, and so the error growth is much larger than would be encountered with normal Gaussian elimination with partial pivoting. A modification of the algorithm to perform a type of row-column pivoting is proposed which may ameliorate this problem.; no

## Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis

Thyer, M.; Renard, B.; Kavetski, D.; Kuczera, G.; Franks, S.; Srikanthan, S.
Fonte: Amer Geophysical Union Publicador: Amer Geophysical Union
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The lack of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall‐runoff (CRR) models remains a key challenge in hydrology. The Bayesian total error analysis (BATEA) methodology provides a comprehensive framework to hypothesize, infer, and evaluate probability models describing input, output, and model structural error. This paper assesses the ability of BATEA and standard calibration approaches (standard least squares (SLS) and weighted least squares (WLS)) to address two key requirements of uncertainty assessment: (1) reliable quantification of predictive uncertainty and (2) reliable estimation of parameter uncertainty. The case study presents a challenging calibration of the lumped GR4J model to a catchment with ephemeral responses and large rainfall gradients. Postcalibration diagnostics, including checks of predictive distributions using quantile‐quantile analysis, suggest that while still far from perfect, BATEA satisfied its assumed probability models better than SLS and WLS. In addition, WLS/SLS parameter estimates were highly dependent on the selected rain gauge and calibration period. This will obscure potential relationships between CRR parameters and catchment attributes and prevent the development of meaningful regional relationships. Conversely...

## Inertial Sensors in Estimating Spatio-Temporal Parameters of Walking: Performance Evaluation and Error Analysis

YANG, SHUOZHI
Fonte: Quens University Publicador: Quens University
EN; EN
Relevância na Pesquisa
55.95%
The portability, ease of use and improved accuracy of miniature inertial sensors brought by current microelectromechanical system (MEMS) technology has inspired researchers to develop human movement monitoring system with body-fixed sensors. Although a large number of studies have attempted to explore the use of miniature inertial sensors in estimating walking speed for the past two decades, there still remain some questions regarding applying inertial sensors in estimating walking speed under different walking conditions and for different subject populations. In this thesis, I focus on evaluating and improving the performance of a shank-mounted mounted inertial measurement unit (IMU) based walking speed estimation method. My research can be divided into four parts. The first part was a systematic review regarding the state of the art of current development of the inertial sensor based walking speed estimation method. A total of 16 articles were fully reviewed in terms of sensor specification, sensor attachment location, experimental design and spatial parameter estimation algorithm. In the second part, a comprehensive performance evaluation was conducted, which included the treadmill and overground walking experiments with constraint on the walking speed...

## A low-order mixed finite element method for a class of quasi-Newtonian Stokes flows. Part II: a posteriori error analysis

González Taboada, María; Gatica, Gabriel N.; Meddahi, Salim
Fonte: Elsevier BV Publicador: Elsevier BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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[Abstract] This is the second part of a work dealing with a low-order mixed finite element method for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. In the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation, and that the corresponding Galerkin scheme becomes well posed with piecewise constant functions and Raviart–Thomas spaces of lowest order as the associated finite element subspaces. In this paper we develop a Bank–Weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions. Several numerical results illustrating the efficiency of the method are also provided.

## Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems

Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.88%
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite element discretization which converges owing to some a priori $L^2$ error estimates even for reduced regularity on non-convex polygonal domains. An equivalence result of that nonconforming finite element scheme to the mixed finite element method (MFEM) leads to the well-posedness of the discrete solution and to a priori error estimates for the MFEM. The explicit residual-based a posteriori error analysis allows some reliable and efficient error control and motivates some adaptive discretization which improves the empirical convergence rates in three computational benchmarks.; Comment: 35 pages, 8 figures

## Backward error analysis and the substitution law for Lie group integrators

Lundervold, Alexander; Munthe-Kaas, Hans
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.81%
Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.; Comment: Minor corrections and additions. Final version

## Global Error Analysis and Inertial Manifold Reduction

Chung, Yu-Min; Steyer, Andrew; Tubbs, Michael; Van Vleck, Erik S.; Vedantam, Mihir
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.93%
Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to rescaling of time. To determine the amplification of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems of equations. We combine these ideas with techniques for dimension reduction of differential equations via a boundary value formulation of numerical inertial manifold reduction. These global error concepts are exercised to illustrate their utility on the Lorenz equations and inertial manifold reductions of the Kuramoto-Sivashinsky equation.

## A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to $C^0$ IP methods

Chowdhury, Sudipto; Gudi, Thirupathi; Nandakumaran, A. K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.87%
In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers reliable and efficient a posteriori error estimators. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posed ness of the problem. Subsequently, applications of $C^0$ interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings. Finally, we also discuss the variational discontinuous discretization method (without discretizing the control) and its corresponding error estimates.; Comment: 23 pages, 5 figures, 1 table

## Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo

Arampatzis, Giorgos; Katsoulakis, Markos A.; Plechac, Petr
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.87%
In this paper we study from a numerical analysis perspective the Fractional Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are fractional step algorithms with a time-stepping window $\Delta t$, and as such they are inherently partially asynchronous since there is no processor communication during the period $\Delta t$. In this contribution we primarily focus on the error analysis of FS-KMC algorithms as approximations of conventional, serial kinetic Monte Carlo (KMC). A key aspect of our analysis relies on emphasising a goal-oriented approach for suitably defined macroscopic observables (e.g., density, energy, correlations, surface roughness), rather than focusing on strong topology estimates for individual trajectories. One of the key implications of our error analysis is that it allows us to address systematically the processor communication of different parallelization strategies for KMC by comparing their (partial) asynchrony, which in turn is measured by their respective fractional time step $\Delta t$ for a prescribed error tolerance.; Comment: 32 pages, 4 figures

## Error analysis of a partial pivoting method for structured matrices

Sweet, Douglas R.; Brent, Richard P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.85%
Many matrices that arise in the solution of signal processing problems have a special displacement structure. For example, adaptive filtering and direction-of-arrival estimation yield matrices of Toeplitz type. A recent method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian elimination with partial pivoting for such structured matrices. In this paper, a rounding error analysis is performed on the Cauchy and Toeplitz variants of the GKO method. It is shown the error growth depends on the growth in certain auxiliary vectors, the generators, which are computed by the GKO algorithms. It is also shown that in certain circumstances, the growth in the generators can be large, and so the error growth is much larger than would be encountered with normal Gaussian elimination with partial pivoting. A modification of the algorithm to perform a type of row-column pivoting is proposed; it may ameliorate this problem.; Comment: 18 pages. An old Technical Report, submitted for archival purposes. For further details see http://wwwmaths.anu.edu.au/~brent/pub/pub157.html

## Robust error analysis of coupled mixed methods for Biot's consolidation model

Lee, Jeonghun J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.87%
We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed finite elements, one for linear elasticity and the other for mixed Poisson problems are coupled for spatial discretization, and we show that any pair of stable mixed finite elements is available. The novelty of our analysis is that the error estimates of all the unknowns are robust for material parameters. Specifically, the analysis does not need a uniformly positive storage coefficient, and the error estimates are robust for nearly incompressible materials. Numerical experiments illustrating our theoretical analysis are included.; Comment: 21 pages

## On an a posteriori error analysis of a mixed finite element Galerkin approximations to a second order wave equation

Karaa, Samir; Pani, Amiya K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.83%
In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker's technique introduced earlier by G. Baker ( SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equation, a posteriori error estimates of the displacement in L{\infty}(L2)-norm for the semidiscrete scheme are derived under minimal regularity. Finally, a first order implicit-in-time discrete scheme is analyzed and a posteriori error estimators are established.

## Optimal Control of a Free Boundary Problem with Surface Tension Effects: A Priori Error Analysis

Antil, Harbir; Nochetto, Ricardo H.; Sodré, Patrick
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.85%
We present a finite element method along with its analysis for the optimal control of a model free boundary problem with surface tension effects, formulated and studied in \cite{HAntil_RHNochetto_PSodre_2014a}. The state system couples the Laplace equation in the bulk with the Young-Laplace equation on the free boundary to account for surface tension. We first prove that the state and adjoint system have the requisite regularity for the error analysis (strong solutions). We discretize the state, adjoint and control variables via piecewise linear finite elements and show optimal $O(h)$ error estimates for all variables, including the control. This entails using the second order sufficient optimality conditions of \cite{HAntil_RHNochetto_PSodre_2014a}, and the first order necessary optimality conditions for both the continuous and discrete systems. We conclude with two numerical examples which examine the various error estimates.

## Error analysis of tau-leap simulation methods

Anderson, David F.; Ganguly, Arnab; Kurtz, Thomas G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.82%
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of the system. We argue that this is a more appropriate scaling than that found in previous error analyses in which the size of the time discretization goes to zero independent of the rest of the model. Under the present scaling, we show that midpoint tau-leaping achieves a higher order of accuracy, in both a weak and a strong sense, than Euler tau-leaping; a result that is in contrast to previous analyses. We present examples that demonstrate our findings.; Comment: Published in at http://dx.doi.org/10.1214/10-AAP756 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## Preasymptotic error analysis of higher order FEM and CIP-FEM for Helmholtz equation with high wave number

Du, Yu; Wu, Haijun
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.83%
A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$- error estimates with explicit dependence on the wave number $k$ are derived. In particular, it is shown that if $k^{2p+1}h^{2p}$ is sufficiently small, then the pollution errors of both methods in $H^1$-norm are bounded by $O(k^{2p+1}h^{2p})$, which coincides with the phase error of the FEM obtained by existent dispersion analyses on Cartesian grids, where $h$ is the mesh size, $p$ is the order of the approximation space and is fixed. The CIP-FEM extends the classical one by adding more penalty terms on jumps of higher (up to $p$-th order) normal derivatives in order to reduce efficiently the pollution errors of higher order methods. Numerical tests are provided to verify the theoretical findings and to illustrate great capability of the CIP-FEM in reducing the pollution effect.

## Unconditionally optimal error analysis of fully discrete Galerkin methods for general nonlinear parabolic equations

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.85%
The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as proposed in \cite{LS1}, we split the error function into two parts, one from the temporal discretization and one the spatial discretization. We prove that the latter is $\tau$-independent and the numerical solution is bounded in the $L^{\infty}$ and $W^{1,\infty}$ norms by the inverse inequalities. With the boundedness of the numerical solution, optimal error estimates can be obtained unconditionally in a routine way. Several numerical examples in two and three dimensional spaces are given to support our theoretical analysis.

## Recovery of North-East Atlantic temperature fields from profiling floats: Determination of the optimal float number from sampling and instrumental error analysis

Ruiz, Simón; Gomis, Damià; Font, Jordi
Tipo: Artículo Formato: 131118 bytes; application/pdf
ENG
Relevância na Pesquisa
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12 pages, 4 figures, 1 table.-- Available online Oct 12, 2006.-- Issue title: "Marine Environmental Monitoring and Prediction - Selected papers from the 36th International Liège Colloquium on Ocean Dynamics" (May 3-7, 2004).-- Full-text version available Open Access at: http://www.icm.csic.es/files/oce/almacen/papers/AR-2007-04.pdf; Argo is an international project that is deploying an array of temperature and salinity profiling floats over the global ocean. Here we use the error formulation derived from Optimal Statistical Interpolation to estimate statistical errors associated with the recovery of the temperature field in the North-East Atlantic ocean. Results indicate that with the present distribution of floats (119 in the considered domain), scales of wavelength larger than 500 km can be recovered with a relative uncertainty (rms error relative to the standard deviation of the field) of about 7% at 50 m, 8% at 200 m and 10% at 1000 m. This corresponds to mean absolute errors of 0.111°C at 50 m, 0.104°C at 200 m and 0.073°C at 1000 m.; The splitting of total errors into instrumental and sampling contributions reveals that, in the present scenario, errors are more due to the small number of floats than to instrumental errors...

## Human reliability analysis in healthcare: Application of the cognitive reliability and error analysis method (CREAM) in a hospital setting

Deeter, Joey
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
EN_US
Relevância na Pesquisa
55.92%
Patient safety is a concern within the healthcare domain as it is estimated that tens of thousands of people die annually from preventable medical errors. For over ten years, traditional Human Reliability Analysis (HRA) techniques (e.g., Root Cause Analysis and Failure Mode and Effect Analysis) have been used in hospitals nationwide in an attempt to explain why these errors occur and what can be done to prevent them. Still, patient safety has not improved significantly. Traditional HRA techniques are limited as analysis tools. They do not consider the context in which workers operate. They are also not based on a valid psychological model that could explain human cognitive function. The Cognitive Reliability and Error Analysis Method (CREAM) is an HRA technique that allows analysts to examine worker actions through the context of performance-shaping factors. The CREAM also employs a cognitive model to explain cognitive failures. This research used the CREAM to re-analyze events containing identifiable error modes that were previously analyzed by hospital team members using the RCA technique. The results of the re-analyses using the CREAM were compared with the previous analyses from RCA events. Additionally, several RCA events were observed and detailed written narratives of the observations were used to perform further independent analyses by three independent analysts in an effort to calculate inter-rater agreement. The results exposed a gap within categories of causal factors between the two techniques. The CREAM identified organizational factors as contributing to error in the events whereas those factors were either minimized or ignored in the RCA. The results also failed to demonstrate any significant inter-rater agreement among independent analysts performing the CREAM analyses. Due to serious data limitations...

## An error analysis in the early grades mathematics - A learning opportunity?

Herholdt,Roelien; Sapire,Ingrid
Fonte: South African Journal of Childhood Education Publicador: South African Journal of Childhood Education
Tipo: Artigo de Revista Científica Formato: text/html