Given a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A+∆A+ μ(E +∆E), one approach for general singular pencils and another one such that A+∆A and E + ∆E have a common left/right...

A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an equivalent matrix pencil – a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P ) that generalize the first and second companion forms have recently been introduced by Mackey, Mackey, Mehl and Mehrmann. Almost all of these pencils are linearizations for P (λ) when P is regular. Th...

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used...

This paper proposes an automated quadrilateral meshing technique based on the conversion of triangular meshes. Given a triangular mesh and a vector eld representing the desired directionality of quadrilateral elements, our new approach generates a well-shaped and well-aligned quadrilateral mesh. In the approach, the values of three scalar functions are rst calculated for each pair of adjacent t...

We present a new extension of the well-known Perron-Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied.

The concept of fairing applied to triangular meshes with irregular connectivity has become more and more important. Previous contributions proposed a variety of fairing operators for manifolds and applied them to design multiresolution representations and editing tools for meshes. In this paper, we generalize these powerful techniques to handle non-manifold models. We propose a method to constr...

In this paper, we designed and implemented a method which can register and integrate range images obtained from different view points for building complete 3D object models. This method contains three major parts: (1) registration of range images and estimation of the parameters of rigid-body transformations, (2) integration of redundant surface patches and generation of triangulated mesh surfa...

Our first motive for this research stems from problems with traditional terrain representations which were recognized as early as 1967 by Boehm. Topographic surfaces are non-stationary (Pike and R-ozema, 1975), i.e., the roughness of the terrain is not periodic but changes from one landtype to another. A regular grid therefore has to be adjusted to the roughest terrain in the mod'el and be high...

This paper tackles a particular shape matching problem: given a data base of shapes (described as triangular meshes), we search for all shapes which describe a human. We do so by applying a 3D face detection approach on the mesh which consists of three steps: first, a local symmetry value is computed for each vertex. Then, the symmetry values in a certain neighborhood of each vertex are analyze...

In this paper, we attempt to reveal the precise relation between the error of linear interpolation on a general triangle and the geometric characters of the triangle. Taking the model problem of interpolating quadratic functions, we derive two exact formulas for the H1-seminorm and L2-norm of the interpolation error in terms of the area, aspect ratio, orientation, and internal angles of the tri...