کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
471311 698619 2014 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A generalization of the optimal diagonal approximate inverse preconditioner
ترجمه فارسی عنوان
تعمیم مطلوب پیش بینی کننده معکوس تقریبی مورب
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
چکیده انگلیسی

The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax=bAx=b is generalized and improved. The new proposed approximate inverse preconditioner NN is based on the minimization of the Frobenius norm of the residual matrix AM−IAM−I, where MM runs over a certain linear subspace of n×nn×n real matrices, defined by a prescribed sparsity pattern. The number of nonzero entries of the n×nn×n preconditioning matrix NN is less than or equal to 2n2n, and nn of them are selected as the optimal positions in each of the nn columns of matrix NN. All theoretical results are justified in detail. In particular, the comparison between the proposed preconditioner NN and the optimal diagonal one is theoretically analyzed. Finally, numerical experiments reported confirm the theory and illustrate that our generalization of the optimal diagonal preconditioner improves (in general) its efficiency, when they do not coincide.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 66, Issue 12, January 2014, Pages 2433–2445
نویسندگان
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