The Nonlinear Problem of the 3d Datum Transformation and the Procrustes Algorithm

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
A special nonlinear problem is the three-dimensional datum transformation solved by the
Procrustes Algorithm. A definition of the three-dimensional datum transformation with the …

The second problem of probabilistic regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
In probabilistic regression we study the determination of first moments as well as second
central moments of type special Gauss–Markov model without Datum Defect. Theoretical …

The First Problem of Algebraic Regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
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The Fifth Problem of Algebraic Regression: The System of Conditional Equations: Homogeneous and Inhomogeneous Equations:

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
The Fifth Problem of Algebraic Regression: The System of Conditional Equations: Homogeneous
and Inhomogeneous Equations: $$\{\mathbf{By} = \mathbf{Bi}\ \mathbf{versus} -\mathbf{c} + …

The Third Problem of Probabilistic Regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
Abstract The Special Gauss-Markov model with datum defect–the stochastic analogue of
Minimum Norm Least-Squares, is treated here first by the Best Linear Minimum Bias …

Special Problems of Algebraic Regression and Stochastic Estimation

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
Up to now, we have only considered an “univariate Gauss–Markov model”. Its generalization
towards a multivariate Gauss–Markov model will be given in Sect. 14.1. At first, we define a …

The First Problem of Probabilistic Regression: The Bias Problem

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
The bias problem in probabilistic regression has been the subject of Sect. 4-37 for
simultaneous determination of first moments as well as second central moments by …

The Fourth Problem of Probabilistic Regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
The random effect model as a special Gauss-Markov model with random effects is an
extension of the classical Gauss-Markov model: both effect, namely the vector y of …

The Third Problem of Algebraic Regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
The optimisation problem which appears in general linear systems and weakly nonlinear
systems is a standard topic in many textbooks on optimization. Here we again define nearly …

The Second Problem of Algebraic Regression

E Grafarend, J Awange, EW Grafarend… - Linear and Nonlinear …, 2012 - Springer
The optimization problem which appears in treating overdetermined linear system equations
is a standard topic in any textbook on optimization. Here we consider again a weak …