TR-2007003: Additive Preconditioning for Matrix Computations
نویسندگان
چکیده
Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations. Our novel SVD-free additive preconditioners are more readily available and better preserve matrix structure. We study their generation and their affect on conditioning of the input matrix. In other papers we combine additive preconditioning with aggregation and other relevant techniques to facilitate the solution of linear systems of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects.
منابع مشابه
TR-2007002: Additive Preconditioning and Aggregation in Matrix Computations
Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations, but our SVD-free additive preconditioners are more readily available and better preserve matrix structure. We combine additive preconditioning with aggregation and other relevant techniques to facilitate the solution of linear systems of equations and some other fundamental matrix c...
متن کاملTR-2006006: Additive Preconditioning and Aggregation in Matrix Computations
Multiplicative preconditioning is a popular tool for handling linear systems of equations provided the relevant information about the associated singular values is available. We propose using additive preconditioners, which are readily available for both general and structured ill conditioned input matrices and which preserve matrix structure. We introduce primal and dual additive preconditioni...
متن کاملTR-2008005: Weakly Random Additive Preconditioning for Matrix Computations
Our weakly random additive preconditioners facilitate the solution of linear systems of equations and other fundamental matrix computations. Compared to the popular SVD-based multiplicative preconditioners, these preconditioners are generated more readily and for a much wider class of input matrices. Furthermore they better preserve matrix structure and sparseness and have a wider range of appl...
متن کاملAdditive preconditioning and aggregation in matrix computations
Multiplicative preconditioning is a popular tool for handling linear systems of equations provided the relevant information about the associated singular values is available. We propose using additive preconditioners, which are readily available for both general and structured ill conditioned input matrices and which preserve matrix structure. We introduce primal and dual additive preconditioni...
متن کاملTR-2007011: Numerical Computation of Determinants with Additive Preconditioning
Various geometric and algebraic computations (e.g., of the convex hulls, Voronoi diagrams, and scalar, univariate and multivariate resultants) boil down to computing the sign or the value of the determinant of a matrix. For these tasks numerical factorizations of the input matrix is the most attractive approach under the present day computer environment provided the rounding errors are controll...
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