Abstract
In this chapter, we will showcase a new approach to the calculation of the extrema of functions in one dimension by implementing the golden-section search algorithm using the dataflow paradigm. This paradigm has been around for quite some time already, but it was only recently, with the increased need to compute large datasets, that its use was brought to attention to many scientists around the globe. BigData has always been present to an extent, but with the ever-growing industry and the increasing speed in which information multiplies by the minute, the models that follow these changes have been expanding as well. Many fields use mathematical models as a way of explanation of various systems. These models are usually composed of equations whose number is counted in thousands. Too often it is needed to calculate the extrema of functions that those equations represent. Doing this the traditional way by using the control-flow paradigm shows that the majority of execution time is spent on calculation. In this chapter, we would like to show that this process can be sped up, and thus, leave more time to perform other actions regarding the exploration of the modeled systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Lyman P, Varian H (2004) How much information 2003? Tech Rep
Fisher D, DeLine R, Czerwinski M, Drucker S (2012) Interactions with big data analytics. Interactions 19(3):50–59
Hurson A, Lee B (1993) Issues in dataflow computing. Adv Comput 37:285–333
Kos A, Toma S, Salom J, Trifunovic N, Valero M, Milutinovic V (2015) New benchmarking methodology and programming model for big data processing. Int J Distrib Sens Netw 11:1–7
Milutinovic V (1996) The best method for presentation of research results. IEEE TCCA Newsl 1–6
Jakus G, Milutinovic V, Omerovic S, Tomazic S (2013) Concepts. Concepts, ontologies, and knowledge representation. Springer, Berlin, pp 5–27
Furht B, Milutinovic V (1987) A survey of microprocessor architectures for memory management. Computer 20:48–67
Milutinovic V (1996) Surviving the design of a 200 MHz RISC microprocessor: lessons learned. IEEE Computer Society, Washington
Milutinovic V (1989) High-level language computer architecture. Computer Science Press Inc., Washington
Milutinovic V, Stenstrom P (1999) Special issue on distributed shared memory systems. Proc IEEE 87:399–404
Trifunovic N, Milutinovic V, Salom J, Kos A (2015) Paradigm shift in big data supercomputing: dataflow vs. controlflow. J Big Data 2:4
Gill PE, Murray W, Wright MH (1981) Practical optimization. Academic Press Inc. (London) Limited, London
Antoniou A, Lu WS (2007) Practical optimization: algorithms and engineering applications. Springer, Berlin
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press, Cambridge
Patron RSF, Botez RM, Labour D (2012) Vertical profile optimization for the flight management system CMA-9000 using the golden section search method. In: IECON 2012-38th annual conference on IEEE industrial electronics society. IEEE, pp 5482–5488
Tsai CH, Kolibal J, Li M (2010) The golden section search algorithm for finding a good shape parameter for meshless collocation methods. Eng Anal Bound Elem 34(8):738–746
Nazareth L, Tseng P (2002) Gilding the lily: a variant of the Nelder-Mead algorithm based on golden-section search. Computational optimization and applications. Springer, Berlin
Dennis JB, Misunas DP (1974) A preliminary architecture for a basic data-flow processor. In: Newsletter ACM SIGARCH Computer Architecture News Homepage, vol 3(4)
Maxeler (2013) Multiscale dataflow programming
Milutinovic V, Salom J, Trifunovic N, Giorgi R (2015) Guide to dataflow supercomputing. Springer, Berlin
Maxeler (2016) Maxeler DFE debugging and optimization tutorial
Kowalik J, Osborne MR (1968) Methods for unconstrained optimization problems. American Elsevier Publishing Company, New York
Wilde DJ (1964) Optimum seeking methods. Prentice Hall, Upper Saddle River
Brent RP (1973) Algorithms for minimization without derivatives. Prentice Hall, Upper Saddle River
Kiefer J (1953) Sequential minimax search for a maximum. Proc Am Math Soc 4(3):502–506
Fu H, Osborne W, Clapp B, Pell O (2008) Accelerating seismic computations on FPGAs from the perspective of number representations. Rome
Trifunovic N, Milutinovic V, Korolija N, Gaydadjiev G (2016) An AppGallery for dataflow computing. J Big Data
Bader DA, Pennington R (2001) Cluster computing: applications. Int J High Perform Comput 15(2):181–185
Blagojevic V et al (2016) A systematic approach to generation of new ideas for PhD research in computing. Advances in computers, vol 104. Elsevier, Amsterdam, pp 1–19
Acknowledgements
The authors would like to thank Professor Milutinovic for inviting us to contribute to this book and for his encouragement throughout this project, as well as Milos Kotlar for providing guidance during the process of writing this work. This research was supported by Maxeler Technologies, Serbia, Belgrade. We want to thank our families, colleagues who provided insight and expertise that greatly assisted the research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Pejic, D., Arsic, M. (2019). Minimization and Maximization of Functions: Golden-Section Search in One Dimension. In: Milutinovic, V., Kotlar, M. (eds) Exploring the DataFlow Supercomputing Paradigm. Computer Communications and Networks. Springer, Cham. https://doi.org/10.1007/978-3-030-13803-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-13803-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13802-8
Online ISBN: 978-3-030-13803-5
eBook Packages: Computer ScienceComputer Science (R0)