A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
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A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...
Usage of the Sherman-Morrison-Woodbury formula to update linear systems after low rank modifications of the system matrix is widespread in machine learning. However, it is well known that this formula can lead to serious instabilities in the presence of ro ...
Any finite, separately convex, positively homogeneous function on R2 is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...
We formulate Euler-Poincare and Lagrange-Poincare equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. Th ...
For a given skew symmetric real n x n matrix N, the bracket X, Y = XNY - YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n x n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to inves ...
Most state-of-the-art algorithms for filament detection in 3-D image-stacks rely on computing the Hessian matrix around individual pixels and labeling these pixels according to its eigenvalues. This approach, while very effective for clean data in which li ...
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...
The contragredient transformation A bar right arrow P-1 AP-(inverted perpendicular) , B bar right arrow P-inverted perpendicular BP of two matrices A, B effects simultaneous similarity transformations of the products AB and BA. This work provides structure ...
Most state-of-the-art algorithms for filament detection in 3-D image-stacks rely on computing the Hessian matrix around individual pixels and labeling these pixels according to its eigenvalues. This approach, while very effective for clean data, hi which l ...
The linear complementarity problem (LCP) is a general problem that unifies linear and quadratic programs and bimatrix games. In this paper, we present an efficient algorithm for the solution to multiparametric linear complementarity problems (pLCPs) that a ...
