In seepage problems, the coefficients of permeability in Laplace equation are usually assumed to be constant vs. both space and time; but in reality these coefficients are variable. In this study, the effect of material deformation due to external loads (consolidation) and variation of head in the consolidation process are considered. For the first case, formulation of kx and ky can be defined ...

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random e...

A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fitting C1 piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examp...

A method is developed for fitting a hyperplane to a set of data by least-squares, allowing for independent uncertainties in all coordinates of each data point, and including an error analysis. Note: This paper is adapted from a technical report I wrote as a graduate student in the Department of Physics, University of California, Berkeley, in 1976. Copyright c ©2002, by Robert K. Moniot. All rig...

Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g. computer graphics [1], coordinate metrology [2], petroleum engineering [11], statistics [7]. In the past, algorithms have been given which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points [1], [6]. In this paper we p...

A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, i.e., these estimators do not converge to the true value of the parameters, as the sample size tends to infinity.A consistent estimato...

This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4 2 1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: (i) It is ellipse-specific so th...

Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g. computer graphics [1], coordinate metrology [2], petroleum engineering [11], statistics [7]. In the past, algorithms have been given which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points [1], [6]. In this paper we p...