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Fundamentals of matrix computations
David S. Watkins
- 01 Jan 1991
TL;DR: This paper focuses on Gaussian Elimination as a model for Iterative Methods for Linear Systems, and its applications to Singular Value Decomposition and Sparse Eigenvalue Problems.
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Abstract: Gaussian Elimination and its Variants Sensitivity of Linear Systems Effects of Roundoff Errors Orthogonal Matrices and the Least Squares Problem Eigenvalues, Eigenvectors and Invariant Subspaces Other Methods for the Symmetric Eigenvalue Problem The Singular Value Decomposition Appendices Bibliography
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Citations
Feature Extraction for Visual Analysis of DW-MRI Data
Thomas Schultz,Hans-Peter Seidel,Holger Theisel +2 more
- 01 Jan 2009
TL;DR: Streamline visualizations are improved by adding features from structural MRI in a way that emphasizes the relation between the two types of data, and the accuracy of streamlines in high angular resolution data is increased by modeling the estimation of crossing fiber bundles as a low-rank tensor approximation problem.
10
A hybrid scaling parameter for the scaled memoryless BFGS method based on the ℓ∞ matrix norm
TL;DR: An upper bound for condition number of the scaled memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) updating formula in the matrix norm is given and a class of choices for the scaling parameter is achieved, including the Oren–Spedicato formula as an especial case and guaranteeing the descent property.
10
An Aggregation-Based Algebraic Multigrid Method for Power Grid Analysis
Pei-Yu Huang,Huan-Yu Chou,Yu-Min Lee +2 more
- 26 Mar 2007
TL;DR: An innovative constructing method of global inter-grid mapping operator is employed to not only enhance the sparsity of coarse grid operator for reducing the computational complexity but also solve the problem with better convergent rate.
Modifying two-sided orthogonal decompositions: algorithms, implementation, and applications
Jesse L. Barlow,Peter A. Yoon +1 more
- 01 Jan 1996
TL;DR: This thesis proposes several algorithms for rank-one updates and downdates to these decompositions with strong stability properties and efficient implementations on high-performance computers.
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