TR-2009009: Solving Linear Systems with Randomized Augmentation
نویسندگان
چکیده
Our randomized preprocessing of a matrix by means of augmentation counters its degeneracy and ill conditioning, uses neither pivoting nor orthogonalization, readily preserves matrix structure and sparseness, and leads to dramatic speedup of the solution of general and structured linear systems of equations in terms of both estimated arithmetic time and observed CPU time.
منابع مشابه
TR-2010009: Solving Linear Systems with Randomized Augmentation II
With a high probablilty our randomized augmentation of a matrix eliminates its rank deficiency and ill conditioning. Our techniques avoid various drawbacks of the customary algorithms based on pivoting and orthogonalization, e.g., we readily preserve matrix structure and sparseness. Furthermore our randomized augmentation is expected to precondition quite a general class of ill conditioned inpu...
متن کاملTR-2011009: Solving Linear Systems of Equations with Randomized Augmentation and Aggregation
Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix A we combine scaled randomized augmentation with aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization and preserve matrix structure and sparseness. In the case of ill conditioned inputs we perform a ...
متن کاملTR-2012007: Solving Linear Systems of Equations with Randomization, Augmentation and Aggregation II
Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...
متن کاملTR-2012004: Solving Linear Systems of Equations with Randomization, Augmentation and Aggregation
Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...
متن کاملTR-2009014: Randomized Preprocessing of Homogeneous Linear Systems
Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our randomized algorithms and extend our approach to solving nonsingular line...
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تاریخ انتشار 2016