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A distributed block approach to solving near-block-diagonal systems with an application to a large macroeconometric model


  • Jon Faust
  • Ralph W. Tryon


This paper demonstrates two advantages of well-known block variants of standard algorithms for solving nonlinear systems. First, if a problem is suf­ficiently close to block-diagonal, block algorithms may offer significant speed advantages on a single processor. Second, block Jacobi algorithms can easily and efficiently be distributed across multiple processors. We illustrate the use of a distributed block Jacobi algorithm to solve a large nonlinear macroe­conometric model. For our application, on a four-processor Unix server, the algorithm achieves a speedup factor of more than 6 over the standard algo­rithm on a single processor. A speedup factor of about 2 is due to the added efficiency of the block algorithm on a single processor, and the remaining factor of 3 results from distributing the work over four processors.

Suggested Citation

  • Jon Faust & Ralph W. Tryon, 1994. "A distributed block approach to solving near-block-diagonal systems with an application to a large macroeconometric model," International Finance Discussion Papers 488, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgif:488

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    References listed on IDEAS

    1. Edison, Hali J. & Marquez, Jaime R. & Tryon, Ralph W., 1987. "The structure and properties of the Federal Reserve Board Multicountry Model," Economic Modelling, Elsevier, vol. 4(2), pages 115-315, April.
    2. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    3. Gilli, Manfred, 1992. "Causal Ordering and Beyond," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 957-971, November.
    4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    5. Raymond Board & Peter A. Tinsley, 1996. "Smart systems and simple agents: industry pricing by parallel rules," Finance and Economics Discussion Series 1996-50, Board of Governors of the Federal Reserve System (U.S.).
    6. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
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    1. Jon Faust & Ralph W. Tryon, 1995. "Block distributed methods for solving multi-country econometric models," International Finance Discussion Papers 516, Board of Governors of the Federal Reserve System (U.S.).

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    Econometric models ; Time-series analysis;


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