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Title:
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FILL-OUT EXPLOITATION ON COMPRESSED ROW STORAGE OF EXTENDED JACOBIANS |
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Author(s):
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Ebadollah Varnik , Uwe Naumann |
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ISBN:
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978-972-8924-30-0 |
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Editors:
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Nuno Guimarães and Pedro Isaías |
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Year:
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2007 |
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Edition:
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Single |
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Keywords:
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Jacobian Accumulation, Extended Jacobian, Compressed Row Storage. |
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Type:
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Poster/Demonstration |
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First Page:
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793 |
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Last Page:
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796 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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Derivatives are essential ingredients of a wide range of numerical algorithms. We focus on a fast accumulation of Jacobian matrices by Gaussian elimination on a statically allocated compressed row storage representation of the extended Jacobian. We compare our algorithm with centered finite difference approximation whose computational complexity increases exponentially with the number of inputs. Our first algorithm uses reverse elimination on compressed row storage scheme. For scalar vector functions is may yield a linear complexity if reusing fill-out memory getting freed during the elimination process. Moreover, our algorithm is faster than Jacobian computation by reverse elimination on a dynamically maintained computational graph. |
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