7 research outputs found

    Management of bilateral idiopathic renal hematuria in a dog with silver nitrate

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    Renal hematuria has limited treatment options. This report describes management of bilateral idiopathic renal hematuria in a dog with surgically assisted installation of 0.5% silver nitrate solution. Initial treatment resulted in freedom from clinical signs or recurrent anemia for 10 months; however, recurrence of bleeding following a nephrectomy resulted in euthanasia

    Geometric methods on low-rank matrix and tensor manifolds

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    In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors

    Enriched Spectral Method for Stiff Convection-Dominated Equations

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    A novel and simple numerical method for stiff convection-dominated problems is studied in presence of boundary or interior layers. A version of the spectral Chevyshev-collocation method enriched with the so-called corrector functions is investigated. The corrector functions here are designed to capture the stiffness of the layers (see the Appendix), and the proposed method does not rely on the adaptive grid points. The extensive numerical results demonstrate that the enriched spectral methods are very accurate with low computational cost
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