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Linear comparative calibration with correlated measurements

Gejza Wimmer, Viktor Witkovský (2007)

Kybernetika

The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the...

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f r c of a given function f : n × m , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope  f r c of a given function f : n × m , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse

Tomasz Górecki, Maciej Łuczak (2013)

International Journal of Applied Mathematics and Computer Science

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this...

Linear distributional differential equations of the second order

Milan Tvrdý (1994)

Mathematica Bohemica

The paper deals with the linear differential equation (0.1) ( p u ' ) ' + q ' u = f ' ' with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

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