The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Endre Suli - One of the best experts on this subject based on the ideXlab platform.
-
adjoint methods for pdes a posteriori Error Analysis and postprocessing by duality
Acta Numerica, 2002Co-Authors: Michael B Giles, Endre SuliAbstract:We give an overview of recent developments concerning the use of adjoint methods in two areas: the a posteriori Error Analysis of finite element methods for the numerical solution of partial differential equations where the quantity of interest is a functional of the solution, and superconvergent extraction of integral functionals by postprocessing.
-
residual free bubbles for advection diffusion problems the general Error Analysis
Numerische Mathematik, 2000Co-Authors: Franco Brezzi, Donatella L Marini, Endre SuliAbstract:We develop the general a priori Error Analysis of residual-free bubble finite element approximations to linear elliptic convection-dominated diffusion problems subject to homogeneous Dirichlet boundary condition. Optimal-order Error bounds are derived in various norms, using piecewise polynomial finite elements of degree greater than or equal to 1.
-
a priori Error Analysis of residual free bubbles for advection diffusion problems
SIAM Journal on Numerical Analysis, 1999Co-Authors: Franco Brezzi, L D Marini, Thomas J R Hughes, A. Russo, Endre SuliAbstract:We develop an a priori Error Analysis of a finite element approximation to the elliptic advection-diffusion equation $-\eps \Delta u + \conv\cdot \nabla u = f$ subject to a homogeneous Dirichlet boundary condition, based on the use of residual-free bubble functions. An optimal order Error bound is derived in the so-called stability-norm \[ \biggl(\eps \|\nabla v\|^2_{L_2(\Omega)} + \sum_{T} h_T\|\conv\cdot \nabla v\|^2_{L_2(T)}\biggr)^{1/2},\] where hT denotes the diameter of element T in the subdivision of the computational domain.
Zhendong Su - One of the best experts on this subject based on the ideXlab platform.
-
automated backward Error Analysis for numerical code
Conference on Object-Oriented Programming Systems Languages and Applications, 2015Co-Authors: Zhoulai Fu, Zhendong SuAbstract:Numerical code uses floating-point arithmetic and necessarily suffers from roundoff and truncation Errors. Error Analysis is the process to quantify such uncertainty in the solution to a problem. Forward Error Analysis and backward Error Analysis are two popular paradigms of Error Analysis. Forward Error Analysis is more intuitive and has been explored and automated by the programming languages (PL) community. In contrast, although backward Error Analysis is more preferred by numerical analysts and the foundation for numerical stability, it is less known and unexplored by the PL community. To fill the gap, this paper presents an automated backward Error Analysis for numerical code to empower both numerical analysts and application developers. In addition, we use the computed backward Error results to also compute the condition number, an important quantity recognized by numerical analysts for measuring how sensitive a function is to changes or Errors in the input. Experimental results on Intel X87 FPU functions and widely-used GNU C Library functions demonstrate that our Analysis is effective at analyzing the accuracy of floating-point programs.
Carolyn Penstein Rose - One of the best experts on this subject based on the ideXlab platform.
-
an interactive tool for supporting Error Analysis for text mining
North American Chapter of the Association for Computational Linguistics, 2010Co-Authors: Elijah Mayfield, Carolyn Penstein RoseAbstract:This demo abstract presents an interactive tool for supporting Error Analysis for text mining, which is situated within the Summarization Integrated Development Environment (SIDE). This freely downloadable tool was designed based on repeated experience teaching text mining over a number of years, and has been successfully tested in that context as a tool for students to use in conjunction with machine learning projects.
Hermann Ney - One of the best experts on this subject based on the ideXlab platform.
-
Towards automatic Error Analysis of machine translation output
Computational Linguistics, 2011Co-Authors: Maja Popovic, Hermann NeyAbstract:Evaluation and Error Analysis of machine translation output are important but difficult tasks. In this article, we propose a framework for automatic Error Analysis and classification based on the identification of actual erroneous words using the algorithms for computation of Word Error Rate (WER) and Position-independent word Error Rate (PER), which is just a very first step towards development of automatic evaluation measures that provide more specific information of certain translation problems. The proposed approach enables the use of various types of linguistic knowledge in order to classify translation Errors in many different ways. This work focuses on one possible set-up, namely, on five Error categories: inflectional Errors, Errors due to wrong word order, missing words, extra words, and incorrect lexical choices. For each of the categories, we analyze the contribution of various POS classes. We compared the results of automatic Error Analysis with the results of human Error Analysis in order to investigate two possible applications: estimating the contribution of each Error type in a given translation output in order to identify the main sources of Errors for a given translation system, and comparing different translation outputs using the introduced Error categories in order to obtain more information about advantages and disadvantages of different systems and possibilites for improvements, as well as about advantages and disadvantages of applied methods for improvements. We used Arabic–English Newswire and Broadcast News and Chinese–English Newswire outputs created in the framework of the GALE project, several Spanish and English European Parliament outputs generated during the TC-Star project, and three German–English outputs generated in the framework of the fourth Machine Translation Workshop.We show that our results correlate very well with the results of a human Error analy- sis, and that all our metrics except the extra words reflect well the differences between different versions of the same translation system as well as the differences between different translation systems.
-
Error Analysis of Statistical Machine Translation Output
Proceedings of the 5th International Conference on Language Resources and Evaluation (LREC'2006), 2006Co-Authors: David Vilar, Luis Fernando D'haro, Jia Xu, Hermann NeyAbstract:Evaluation of automatic translation output is a difficult task. Several performance measures likeWord Error Rate, Position Independent Word Error Rate and the BLEUand NIST scores are widely use and provide a useful tool for comparing different systems and to evaluate improvements within a system. However the interpretation of all of these measures is not at all clear, and the identification of the most prominent source of Errors in a given system using these measures alone is not possible. Therefore some Analysis of the generated translations is needed in order to identify the main problems and to focus the research efforts. This area is however mostly unexplored and few works have dealt with it until now. In this paper we will present a framework for classification of the Errors of a machine translation system and we will carry out an Error Analysis of the system used by the RWTH in the first TC-STAR evaluation.
M J White - One of the best experts on this subject based on the ideXlab platform.
-
thin sample measurements and Error Analysis of high temperature coaxial dielectric probes
IEEE Transactions on Microwave Theory and Techniques, 1997Co-Authors: S Bringhurst, M F Iskander, M J WhiteAbstract:A metallized-ceramic probe has been designed for high-temperature broad-band dielectric properties measurements. The probe has been used to make complex dielectric properties measurements over the complete frequency band from 500 MHz to 3 GHz, and up to temperatures as high as 1000/spl deg/C. In this paper, we investigate new aspects of the development and utilization of this high-temperature dielectric probe. The first aspect is related to the results of an uncertainty Analysis which was performed to quantify the Errors due to the differential thermal expansion between the inner and outer conductors of metal coaxial probes. In this case, a two-dimensional (2-D) cylindrical finite-difference time-domain (FDTD) code was developed and used for this Analysis. The obtained results were compared and shown to be in good agreement with Error-Analysis data based on analytical solutions for the special case when an air gap exists between the probe and the material under test. Additional new Error-Analysis results show that differential thermal expansions and rough surfaces cause considerable Errors in these measurements, and the use of probes of small differential thermal expansions, such as the developed metallized-ceramic probe, is essential for obtaining accurate results. We also used FDTD numerical simulations to help investigate the use of this probe for the nondestructive complex-permittivity measurements of electrically "thin" samples. It is shown that by backing the material under test with a standard material of known dielectric constant, such as air or metal, the complex permittivity of thin samples can be accurately measured. The other new development is related to the use of the developed metallized-ceramic probe to measure the dielectric properties of thin samples at high temperature and over a broad frequency band. With the developed knowledge from the Error Analysis, and the new FDTD code for thin-sample measurements, the metallized-ceramic probe was used to measure dielectric properties of thin Al/sub 2/O/sub 3/ and sapphire samples for temperatures up to 1000/spl deg/C. This measurement method has important applications in the on-line characterization of semiconductor wafers. Results from the high-temperature thin-sample measurements and the uncertainty Analysis are presented.
