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A matrix lower bound

Description: A matrix lower bound is defined that generalizes ideas apparently due to S. Banach and J. von Neumann. The matrix lower bound has a natural interpretation in functional analysis, and it satisfies many of the properties that von Neumann stated for it in a restricted case. Applications for the matrix lower bound are demonstrated in several areas. In linear algebra, the matrix lower bound of a full rank matrix equals the distance to the set of rank-deficient matrices. In numerical analysis, the ra… more
Date: February 4, 2002
Creator: Grcar, Joseph F.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Algebraic mesh quality metrics

Description: Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix … more
Date: April 24, 2000
Creator: Knupp, Patrick
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Tetrahedral mesh improvement via optimization of the element condition number

Description: The authors present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, they formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the t… more
Date: May 22, 2000
Creator: Freitag, Lori A. & Knupp, Patrick
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
open access

Matrix Norms and the Condition Number: A General Framework to Improve Mesh Quality via Node-Movement

Description: Objective functions for unstructured hexahedral and tetrahedral mesh optimization are analyzed using matrices and matrix norms. Mesh untangling objective functions that create valid meshes are used to initialize the optimization process. Several new objective functions to achieve element invertibility and quality are investigated, the most promising being the ''condition number''. The condition number of the Jacobian matrix of an element forms the basis of a barrier-based objective function tha… more
Date: September 27, 1999
Creator: Knupp, Patrick
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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