A matrix-matrix multiplication approach to the automatic differentiation and parallelization of straight-line codes.

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A Straight-line code, which consists of assignment, addition, and multiplication statements is an abstraction of a serial computer program to compute a function with n inputs. Given a serial straight-line code with N statements, the authors derive an algorithm that automatically evaluates not only the function but also its first-order derivatives with respect to the n inputs on a parallel computer. The basic idea of the algorithm is to marry automatic computation of derivatives with automatic parallelization of serial programs. The algorithm requires O(M{sub N} log of N) scalar operations, where O(M{sub N}) is the time complexity of a parallel ... continued below

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15 pages

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Buecker, H. M.; Buschelman, K. R. & Hovland, P. D. November 16, 2000.

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A Straight-line code, which consists of assignment, addition, and multiplication statements is an abstraction of a serial computer program to compute a function with n inputs. Given a serial straight-line code with N statements, the authors derive an algorithm that automatically evaluates not only the function but also its first-order derivatives with respect to the n inputs on a parallel computer. The basic idea of the algorithm is to marry automatic computation of derivatives with automatic parallelization of serial programs. The algorithm requires O(M{sub N} log of N) scalar operations, where O(M{sub N}) is the time complexity of a parallel multiplication of two dense N x N matrices and it represents a measure of the complexity of the straight-line code. Although it can be exponential in N in the worse case, it tends to be only polynomial in N for many important problems.

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15 pages

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  • International Conference on Architecture of Computing Systems (ARCS 2002), Karlsruhe (DE), 04/08/2002--04/11/2002

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  • Report No.: ANL/MCS/CP-103441
  • Grant Number: W-31-109-ENG-38
  • Office of Scientific & Technical Information Report Number: 801570
  • Archival Resource Key: ark:/67531/metadc742420

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  • November 16, 2000

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  • Oct. 19, 2015, 7:39 p.m.

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  • March 25, 2016, 12:16 p.m.

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Buecker, H. M.; Buschelman, K. R. & Hovland, P. D. A matrix-matrix multiplication approach to the automatic differentiation and parallelization of straight-line codes., article, November 16, 2000; Illinois. (digital.library.unt.edu/ark:/67531/metadc742420/: accessed August 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.