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Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
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- Finite element method (3)
- Inverse problems (3)
- Superconvergence (3)
- Boundary element. (2)
- Boundary quadrature formula (2)
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- Gradient recovery (2)
- Impedance imaging (2)
- Least-squares fitting (2)
- ZZ patch recovery (2)
- A posteriori error estimate (1)
- A posteriori error estimates (1)
- Asymptotically efficient (1)
- Asymptotically linear estimator (1)
- Bivariate current status data (1)
- Causal inference (1)
- Cluster analysis (1)
- Coarsening at random (1)
- Crack detection (1)
- Gene expression (1)
- Influence curve (1)
- Inverse probability of treatment weighted estimators (1)
- Marginal structural models (1)
- Non-destructive testing (1)
- Nondestructive testing (1)
- Observational studies (1)
- One-step estimator (1)
- PPR (1)
- Quadrilateral mesh (1)
- Regression (1)
- Reipocity gap (1)
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Articles 1 - 13 of 13
Full-Text Articles in Numerical Analysis and Computation
An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan
An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …
A Review Of Selected Works On Crack Indentification, Kurt M. Bryan
A Review Of Selected Works On Crack Indentification, Kurt M. Bryan
Mathematical Sciences Technical Reports (MSTR)
We give a short survey of some of the results obtained within the last 10 years or so concerning crack identification using impedance imaging techniques. We touch upon uniqueness results, continuous dependence results, and computational algorithms.
Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah
Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah
Mathematical Sciences Technical Reports (MSTR)
We examine the inverse problem of locating and describing an internal point defect in a one dimensional rod W by controlling the heat inputs and measuring the subsequent temperatures at the boundary of W. We use a variation of the forward heat equation to model heat flow through W, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.
Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela
Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela
Mathematical Sciences Technical Reports (MSTR)
We examine the problem of Identifying both the location and constitutive law governing electrical current flow across a one-dimensional linear crack in a two dimensional region when the crack only partially blocks the flow of current. We develop a a constructive numerical procedure for solving the inverse problem and provide computational examples.
Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell
Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell
U.C. Berkeley Division of Biostatistics Working Paper Series
In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …
A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga
A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga
Mathematics Research Reports
Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.
Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang
Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang
Mathematics Research Reports
A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.
Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger
Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger
Mathematical Sciences Technical Reports (MSTR)
This paper develops a fast algorithm for locating one or more perfectly insulating, pair-wise disjoint, linear cracks in a homogeneous two-dimensional electrical conductor, using boundary measurements.
Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang
Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang
Mathematics Research Reports
Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.
A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga
A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga
Mathematics Research Reports
A new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergence at element edge centers for the regular pattern.
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
U.C. Berkeley Division of Biostatistics Working Paper Series
Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …
Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He
Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He
Scholarship
This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.
Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He
Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He
Tian-Xiao He
This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.