Error analysis (mathematics) (Total 932875 Papers Found)

A complete error analysis is performed for the spectral-Galerkin approximation of a model Helmholtz equation with high wave numbers. The analysis presented in this paper does not rely on the explicit knowledge of continuous/discrete Green’s functions and does not require any mesh condition to be satisfied. Furthermore, new error estimates are also established for multidimensional radial and spherical symmetric domains. Illustrative numerical results in agreement with the theoretical analysis a ...
This paper describes a method to upgrade projective reconstruction to a ne and to metric reconstructions using rigid general or planar motions of a stereo rig. We make clear the algebraic relationships between projective reconstruction, the plane at in nity (a ne reconstruction), camera calibration, and metric reconstruction when a 3-D scene is observed with a moving stereo rig. Based on an in-depth algebraic analysis we show that all the computations can be carried out using standard linear res ...
We introduce a new finite element method for the approximation of the three-dimensional Brinkman problem formulated in terms of the velocity, vorticity, and pressure fields. The proposed strategy exhibits the advantage that, at the continuous level, a complete decoupling of vorticity and pressure can be established under the assumption of sufficient regularity. The velocity is then obtained as a simple postprocess from vorticity and pressure, using the momentum equation. Well-posedness follows s ...
In this thesis we develop an adaptive finite element method for pricing of several path-dependent options including barrier options, lookback options, and Asian options. The options are priced using the Black-Scholes PDE-model, and the resulting PDE:s are of parabolic type in one spatial dimension with different boundary conditions and jump conditions at monitoring dates. The adaptive finite element method is based on piecewise polynomial approximations in space and time. We derive a posteriori ...
  • Zhou Jun, Wu Shao-zhi, Wang Yan,
  • 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC)
  • 2011
A method of measuring the PT secondary voltage drop based on GPS is introduced, Because it get the reference time through GPS, two instrument in different place can collect data at the same time. Take no account of harmonic and the magnetic disturbance which affect the voltage acquisition, This article analyzed the distinction error caused by ADC accuracy and the data numbers which are sampled in one period of the signal; and analyzed the angular difference error caused by the GPS's accuracy of ...
We consider a class of multiuser optimization problems in which user interactions are seen through congestion cost functions or coupling constraints. Our primary emphasis lies on the convergence and error analysis of distributed algorithms in which users communicate through aggregate user information. Traditional implementations are reliant on strong convexity assumptions, require coordination across users in terms of consistent stepsizes, and often rule out early termination by a group of users ...
Least-squares principles applied to prediction and objective analyses are discussed. In prediction analysis we investigate the linear, linear weighted and nonlinear methods. Error weights have been taken into account in the linear weighted method. Numerical data are generated by a set of nonlinear equations. Averaged reductions of variance are used to test the advantages of all the schemes. The goodness of the prediction formula depends on the data interval involved but is nearly independent of ...
A common and important problem in business is the determination of inventory policies for a production system within a changing business environment and market demand. In this paper, an automatic pipeline feedback order-based production control system (APIOBPCS), considering a demand with cyclic and stochastic components, is proposed. The dynamics and delays of the production process are modeled as a pure delay. The control system structure consists of a PID (Proportional, Integrative and Deriva ...
This paper investigates a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on non-rectangular domains. The scheme utilizes the shape functions of the moving least squares (MLS) approximation constructed on scattered points as a basis in the discrete collocation method. The MLS methodology is an effective technique for approximating unknown functions which involves a locally weighted least square polynomial fitting. The proposed method is meshl ...
We employ a data-sparse, recursive matrix representation, so-called H 2-matrices, for the efficient treatment of discretized integral operators. We obtained this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators of order zero. In par ...
XML database query languages have been studied extensively, but XML database updates have received relatively little attention, and pose many challenges to language design. We are developing an XML update language called FLUX, which stands for FunctionaL Updates for XML, drawing upon ideas from functional programming languages. In prior work, we have introduced a core language for FLUX with a clear operational semantics and a sound, decidable static type system based on regular expression types. ...
In this paper, a new iterative method is proposed for solving linear integral equations. This method is based on the LSQR method, an algorithm for sparse linear equations and sparse least squares, reducing the solution of linear integral equations to the solution of a bidiagonal linear system of algebraic equations. A simple recurrence formula is presented for generating the sequence of approximate solutions. Some theoretical properties and error analysis of the new method are discussed. Althoug ...
FIR filtering is one of the most populars DSP algorithms. Finite impulse response filters are easy to design, unconditionally stable, phase linearity is easily obtained. Also noise and rounding error analysis are easy. On the other hand FIR filters require high filter order when compared to IIR ones. It means increased number of multiplicatons and additions, and – what is also important – number of memory reads. Current processors and especially their SIMD units like AltiVec or SSE can perfo ...
This paper proposes a piecewise constant time discontinuous Galerkin method to solve the initial-boundary value problem for the heat equation. The finite element is formulated in terms of continuous approximation functions in space directions and piecewise constant approximation functions in time direction. The error analysis for this method in L<inf>2</inf> norm is established, and some numerical examples are included to validate the theoretical analysis. ...
The phenomenon of roundoff-error propagation is a well known problem in computations involving floating point arithmetic. Prominent works in the field of error analysis include (1) the error-analysis based on differential error-propagation model for computer algebra system (CAS), (2) the identification and reformulation of instability in a code generated by CAS, (3) estimating the bounds on errors in symbolic and numerical environments. The main concern in these attempts is to control error-prop ...
In this paper, we describe proximal gradient temporal difference learning, which provides a principled way for designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not with respect to their original objective functions as previously attempted, but rather with respect to primal-dual saddle-point objective functions. We also conduct a saddle-point error analysis to obtain fini ...
We consider approximate solutions to nonlinear hyperbolic conservation laws. If the exact solution is unavailable, the truncation error may be the only quantitative measure for the quality of the approximation. We propose a new way of estimating the local truncation error, through the use of localized test-functions. In the convex scalar case, they can be converted into L∞loc estimates, following the Lip′ convergence theory developed by Tadmor et al. Comparisons between the local truncation ...
This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via a level-set function. The discontinuities are accounted for by using suitable extension operators whose numerical implementation requires a very low computational effort. After carrying out the error analysis, numerical results to validate our ...
This contribution is concerned with the development, analysis and implementation of Adaptive Finite Element Methods (AFEMs) for distributed and boundary control problems with control constraints. AFEMs consist of successive loops of the cycle ’SOLVE’, ’ESTIMATE’, ’MARK’, and ’REFINE’. Emphasis will be on the steps ’SOLVE’ and ’ESTIMATE’. In this context, ’SOLVE’ stands for the efficient solution of the finite element discretized problems and the following step ’ESTI ...
This paper presents an error estimate in the L2-norm for the discontinuous Galerkin finite element methods (DGFEM) for elliptic problems with low regularity solutions. The Raviart–Thomas interpolation operator is employed to derive the new result, which complements the mesh-dependent energy norm error estimates in Gudi (2010) [2]. Numerical results corroborate the theoretical analysis. © 2012 Elsevier Ltd. All rights reserved. 1. DGFEM for elliptic problems The discontinuous Galerkin (DG) fin ...
Task and error analysis research was performed to identify: a) the process for healthcare organisations in managing healthcare for patients with mental illness or substance abuse; b) how the process can be enhanced and; c) if electronic medical records (EMRs) have a role in this process from a business and safety perspective. The research question is if EMRs have a role in enhancing the healthcare for patients with mental illness or substance abuse. A discussion on the business of EMRs is addres ...
We discover a pronounced dependence of the strength of the soft X-ray orbital modulation in Cyg X-1 in the hard state on its superorbital phase. We find our results can be well modelled as orbital-phase dependent X-ray absorption in an accretion bulge, located at the accretion disc edge close to the companion but displaced from the line connecting the stars by about 25◦ and in the case when the disc is precessing (which appears to cause the superorbital flux modulation). Our finding are suppor ...
In this paper, we extend the well known QR-updating scheme to a similar but more versatile and generally applicable scheme for updating the singular value decomposition (SVD). This is done by supplementing the QR-updating with a Jacobi-type SVD procedure, where apparently only a few SVD steps after each QR-update su ce in order to restore an acceptable approximation for the SVD. This then results in a reduced computational cost, comparable to the cost for merely QR-updating. We examine the usefu ...
A VLSI architecture for fast and accurate floating-point sine/cosine evaluation is presented, combining floating-point and simple fixed-point arithmetic. The algorithm implemented by the architecture is based on second-order polynomial interpolation within an approximation interval which is partitioned into regions of unequal length. The exploitation of certain properties of the trigonometric functions and of specific bit patterns that appear in the involved computations, has led to reduced memo ...
Using only algebra, this exposition presents the concept of backward analysis. Numerical examples from finance demonstrate how backward analysis guarantees that the computed value of a polynomial of degree exceeding thirty-one million is accurate to all but the penultimate digit, despite a hundred million intermediate rounding errors. Methods from celestial mechanics then provide initial estimates for the solution of financial polynomial equations. The same analysis applies to the computation of ...
Large spatial gradients in ionosphere delay are a potentially threatening error source for the Local Area Augmentation System (LAAS). Therefore a better understanding of the ionosphere behavior during strong magnetic storms is crucial for LAAS so that it can more accurately evaluate its integrity and availability during these events. In order to obtain spatially-dense information on severe ionosphere delays, we use data from the Japan GPS Earth Observation Network (GEONET). GEONET is a very dens ...
The one-dimensional linear Time Difference Of Arrival (TDOA) location technique is proposed to study the propagation of the acoustic emission signal on the outer ring of the RV reducer. In this paper, we perform the lead break experiments on the outer cylinder bearing of the RV reducer and use the threshold analysis method to calculate the difference of arriving times on sensors. The propagation speed of the signal in the outer race of the bearing is also measured. We find the location of the AE ...
Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared ...
We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in Rydberg (Rydberg 1997), and is based on sampling three independent uniform variables. We apply the algorithm to three problems appearing in finance. First, we consider the valuation of plain vanilla call options and Asian options. The next application considers the problem of deriving implied parameters for the underly ...
Perturbation theory is developed for the Cholesky decomposition of an n × n symmetric positive semi-definite matrix A of rank r. The matrix W = A 11 A12 is found to play a key role in the perturbation bounds, where A11 and A12 are r × r and r × (n − r) submatrices of A respectively. A backward error analysis is given; it shows that the computed Cholesky factors are the exact ones of a matrix whose distance from A is bounded by 4r(r + 1) ( ‖W‖2+1 )2 u‖A‖2+O(u), where u is the unit ro ...
Building energy consumption monitoring and management system plays a vital role in the advance of building energy conservation, because it offers abundant online real time data, which are mainly used to further analyze energy saving potential and put forward a feasibility methodology for implementation. In addition to its extreme importance in decreasing energy consumption and saving costs, the platform can also help to find the anomalies of the main equipment. In this paper, we first introduce ...
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure μ. We show that the average of regular enough test functions with respect to the (possibly non unique) invariant laws of the approximations are close to the corresponding quantity for μ. More precisely, we analyze the rate of the convergence with respect to the different discretization parameters. Here we focus on the discretization in t ...
In this paper we consider heteroclinic orbits in discrete time dynamical systems that connect a hyperbolic fixed point to a non-hyperbolic fixed point with a one-dimensional center direction. A numerical method for approximating the heteroclinic orbit by a finite orbit sequence is introduced and a detailed error analysis is presented. The loss of hyperbolicity requires special tools for proving the error estimate – the polynomial dichotomy of linear difference equations and a (partial) normal ...
Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k–«—two equation turbulence closure, and k–v—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth ...
A Classification Model for Human Error in Collaborative Systems The primary focus of the work reported in this thesis is to investigate and provide a means by which the occurrence of human error in collaborative systems can be better understood. The thesis suggests that much can be gained from looking at human error from a collaborative perspective as opposed to more traditional cognitive and behavioural approaches. The work is motivated through the failure of many human error analysis methodolo ...
Mobile differential optical absorption spectroscopy (mobile DOAS) is an optical remote sensing method that can rapidly measure trace gas emission flux from air pollution sources (such as power plants, industrial areas, and cities) in real time. Generally, mobile DOAS is influenced by wind, drive velocity, and other factors, especially in the usage of wind field when the emission flux in a mobile DOAS system is observed. This paper presents a detailed error analysis and NOx emission with mobile D ...
We present a validation methodology for a cross-linguistic grammar resource which produces output in the form of small grammars based on elicited typological descriptions. Evaluating the resource entails sampling from a very large space of language types, the type and range of which preclude the use of standard test suites development techniques. We produce a database from which gold standard test suites for these grammars can be generated on demand, including well-formed strings paired with all ...
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  • 2012
X-ray diffraction patterns of liquid H g I n alloys with 5, 12, 25, 35, 42, 50 and 62 atomic percent In were measured at room temperature (25 ° C ) . The interference and radial distribution functions, / ( £ ) and 4 JI r2 £ (r ) , respectively, were refined by an error analysis program. The position ^ = 4 n sin &JX of the first peak maximum of I (K) does not change upon alloying, i . e . , ATj = 2.29 A T h e interference function of In plotted in reduced coordinates K / K t agrees with that c ...
In stepped-frequency radar, target motions produce range-profile distortions. Range shift, signal-to-noise ratio loss, and symmetric spreading are produced by target radial velocity, whereas target radial acceleration is mainly responsible for asymmetric smearing. Acceleration-distortion effects are usually negligible when a high Pulse Repetition Frequency (PRF) is used, although this is not the case for low-PRF radars. In this paper, a new motion-compensation technique based on contrast optimiz ...
Abstract Research on corn ethanol is overly focused on whether corn ethanol is a net energy yielder and, consequently, has missed some other fundamental issues, including (1) whether there is significant error associated with current estimates of the EROI of corn ethanol, (2) whether there is significant spatial variability in the EROI of corn ethanol production, (3) whether yield increases will translate linearly to increases in EROI, (4) the extent to which assumptions about co-product credits ...
This paper overviews FBK’s participation in the Textual Entailment task at EVALITA 2009. Our runs were obtained through different configurations of EDITS (Edit Distance Textual Entailment Suite), the first freely available open source tool for Recognizing Textual Entailment (RTE). With a 71% Accuracy, EDITS reported the best score out of the 8 submitted runs. We describe the sources of knowledge that have been used (e.g. extraction of rules from Wikipedia), the different algorithms applied (i. ...
In this thesis, we investigate dependency parsing for commercial application, namely for future integration in a dialogue system. To do this, we conduct several experiments on dialogue data to assess parser performance on this domain, and to improve this performance over a baseline. This work makes the following contributions: first, the creation and manual annotation of a gold-standard data set for dialogue data; second, a thorough error analysis of the data set, comparing neural network parsin ...
The LBL Magnetic Measurements Engineering (MME) Group has developed a Real-Time Data Acquisition System (DAS) for magnetic measurements. The design objective was for a system that was versatile, "portable," modular, expandable, quickly and easily reconfigurable both in hardware and software, and inexpensive. All objectives except the last were attained. An LSI 11/23 microcomputer is interfaced to a clock-calendar, printer, CRT control terminal, plotter with hard copy, floppy and hard disks, GPIB ...
Due to the scarcity of labeled data, most melody extraction algorithms do not rely on fully data-driven processing blocks but rather on careful engineering. For example, the Melodia melody extraction algorithm employs a pitch contour selection stage that relies on a number of heuristics for selecting the melodic output. In this paper we explore the use of a discriminative model to perform purely datadriven melodic contour selection. Specifically, a discriminative binary classifier is trained to ...
In this paper we describe and evaluate a top-down transfer component of a hybrid example-based machine translation system with an architecture similar to that of transfer MT systems, but with automatically derived transfer-rules and dictionary entries based on a parallel treebank. The tests were applied on the translation pair Dutch to English. Evaluation and error analysis have shown that the top-down transfer process has a number of shortcomings on which we wish to report and which we will try ...
Lorenz Plot is widely used in analysis of heart rate variability because of its high sensitivity and high individuation. However, due to the high computational complexity and excessive reliance on experience based tuning, the effectiveness and accuracy of the traditional analysis methods based on Lorenz Plot are both low. In this paper, an automatic detection method according to the shape of Lorenz Plot is proposed, and a sequence of error analysis has been conducted according to the experimenta ...
We present a new multiscale/stabilized finite element method for compressible and incompressible elasticity. The multiscale method arises from a decomposition of the displacement field into coarse (resolved) and fine (unresolved) scales. The resulting stabilizedmixed form consistently represents the fine computational scales in the solution and thus possesses higher coarse mesh accuracy. The ensuing finite element formulation allows arbitrary combinations of interpolation functions for the displ ...
A hybrid direct-sequence (DS)-multiband ultra-wideband (UWB) multiple access system is proposed and a simple error analysis is presented for the system considering a multipath channel. The error analysis facilitates to obtain simple-to-evaluate Improved Gaussian approximation (SIGA), a method that has previously mainly been used in DS-CDMA. In this paper, we show that the method can also be used effectively for UWB multiple access systems. It is shown that despite having the same processing gain ...
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pairpotential interactions, in the presence of vacancy defects. We establish first-order consistency and stability of the method, from which we a priori error estimates in the H-norm and the energy in terms of the mesh size and the “smoothness” of the atomistic solution in the continuum region. From these error estim ...