Abstract
In this paper we discuss a parallel variant of the interval Newton method for root finding of non linear continuously differentiable functions on the CUDA architecture. For this purpose we have investigated different dynamic load balancing methods to get an evenly balanced workload during the parallel computation. We tested the functionality, correctness and performance of our implementation in different case studies and compared it with other implementations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arora, N.S., Blumofe, R.D., Plaxton, C.G.: Thread scheduling for multiprogrammed multiprocessors. In: Proceedings of the Tenth Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1998, pp. 119–129. ACM, New York (1998)
Boost Interval Arithmetic Library (November 2012), http://www.boost.org/doc/libs/1_52_0/libs/numeric/interval/doc/interval.htm
Cederman, D., Tsigas, P.: On dynamic load balancing on graphics processors. In: Proceedings of the 23rd ACM SIGGRAPH/EUROGRAPHICS Symposium on Graphics Hardware, GH 2008, pp. 57–64. Eurographics Association, Aire-la-Ville (2008)
Gau, C.-Y., Stadtherr, M.A.: Parallel interval-newton using message passing: dynamic load balancing strategies. In: Proceedings of the 2001 ACM/IEEE Conference on Supercomputing (CDROM), Supercomputing 2001, pp. 23–23. ACM, New York (2001)
Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: C++ Toolbox for Verified Computing I: Basic Numerical Problems. Springer, Heidelberg (1995)
Jason Sanders, E.K.: CUDA by Example: An Introduction to General-Purpose GPU Programming. Addison-Wesley Longman, Amsterdam (2010)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis, 1st edn. Springer, Heidelberg (2001)
Khronos OpenCL Working Group. The OpenCL Specification, version 1.1.44 (June 2011)
Lerch, M., Tischler, G., Wolff von Gudenberg, J., Hofschuster, W., Krämer, W.: Filib++, a fast interval library supporting containment computations. ACM Trans. Math. Softw. 32(2), 299–324 (2006)
Message Passing Interface Forum. Mpi: A message-passing interface standard, version 2.2. Specification (September 2009)
NVIDIA. NVIDIA CUDA reference manual, version 3.2 Beta (August. 2010)
Tzeng, S., Patney, A., Owens, J.D.: Task management for irregular-parallel workloads on the gpu. In: Doggett, M., Laine, S., Hunt, W. (eds.) High Performance Graphics, pp. 29–37. Eurographics Association (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beck, PD., Nehmeier, M. (2013). Parallel Interval Newton Method on CUDA. In: Manninen, P., Öster, P. (eds) Applied Parallel and Scientific Computing. PARA 2012. Lecture Notes in Computer Science, vol 7782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36803-5_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-36803-5_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36802-8
Online ISBN: 978-3-642-36803-5
eBook Packages: Computer ScienceComputer Science (R0)