Gaussian elimination: when is scaling beneficial?
نویسندگان
چکیده
منابع مشابه
How Accurate is Gaussian Elimination?∗
J.H. Wilkinson put Gaussian elimination (GE) on a sound numerical footing in the 1960s when he showed that with partial pivoting the method is stable in the sense of yielding a small backward error. He also derived bounds proportional to the condition number κ(A) for the forward error ‖x − x̂‖, where x̂ is the computed solution to Ax = b. More recent work has furthered our understanding of GE, la...
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As the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers. We give an overview of GE, ranging from theory to computation. We explai...
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11. Bruening-Wright, A., Elinder, F. & Larsson, H. P. J. Gen. Physiol. 130, 71–81 (2007). 12. Kosta, S. P. et al. Int. J. Med. Eng. Informatics 3, 16–29 (2011). 13. Reich, H. J. & Depp, W. A. J. Appl. Phys. 9, 421 (1938). 14. Francis, V. Fundamentals of Discharge Tube Circuits (Methuen, 1948). 15. Richardson, O. W. The Emission of Electricity from Hot Bodies 1st edn, 304 (Longmans, Green and co...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90382-k