We investigate the geometry of that function in the plane or 3-space, which associates to each point the square of the shortest distance to a given curve or surface. Particular emphasis is put on second order Taylor approximants and other local quadratic approximants. Their key role in a variety of geometric optimization algorithms is illustrated at hand of registration in Computer Vision and s...

Adaptive inverse models find applications in communication and magnetic channel equalization, recovery of digital data and adaptive linearization of sensor characteristics. In presence of outliers in the training signal, the model accuracy is severely reduced. In this paper three robust inverse models are developed by recursively minimizing robust norms using BFO based learning rule. The perfor...

A theorem is presented relating the squared multiple correlation of each measure in a battery with the other measures to the unique generalized inverse of the correlation matrix. This theorem is independent of the rank of the correlation matrix and may be utilized for singular correlation matrices. A coefficient is presented which indicates whether the squared multiple correlation is unity or n...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

If X is a convex surface in a Euclidean space, then the squared intrinsic distance function dist(x, y) is DC (d.c., delta-convex) on X×X in the only natural extrinsic sense. An analogous result holds for the squared distance function dist(x,F ) from a closed set F ⊂ X. Applications concerning r-boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface...

Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to separate clusters. For given training data and a given metric distance, by maximizing the proposed se...

 Abstract: This study deals with modeling of heat flux at the external surface of combustion chamber wall in an internal combustion (IC) engine as a function of crank angle. This investigation results in an inverse heat conduction problem in the cylinder wall. Alifanov regularization method is used for solving this inverse problem. This problem study as an optimization problem in which a square...