메뉴 건너뛰기




Volumn 30, Issue 11, 2011, Pages 1691-1704

Bounding variable values and round-off effects using handelman representations

Author keywords

Algorithms implemented in hardware; numerical analysis; optimization; performance analysis and design aids

Indexed keywords

ALGEBRAIC OPERATIONS; ALGORITHMS IMPLEMENTED-IN-HARDWARE; CONJUGATE GRADIENT ALGORITHMS; EXECUTION TIME; HARDWARE DESIGN; MEMORY USAGE; PERFORMANCE ANALYSIS AND DESIGN AIDS; WORD LENGTH;

EID: 80054822116     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2011.2161307     Document Type: Article
Times cited : (22)

References (38)
  • 1
    • 34548206782 scopus 로고    scopus 로고
    • Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems)
    • J. Langou, P. Luszczek, J. Kurzak, A. Buttari, and J. Dongarra, "Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems)," in Proc. ACM/IEEE Conf. Supercomput., 2006, p. 113.
    • (2006) Proc. ACM/IEEE Conf. Supercomput. , pp. 113
    • Langou, J.1    Luszczek, P.2    Kurzak, J.3    Buttari, A.4    Dongarra, J.5
  • 2
    • 77951160946 scopus 로고    scopus 로고
    • NVIDIA Corporation, Jan, [Online]. Available
    • NVIDIA Corporation. (2009, Jan.). Tesla c1060 Computing Processor Board [Online]. Available: http://www.nvidia.com/docs/IO/43395/BD-04111-001-v05.pdf
    • (2009) Tesla c1060 Computing Processor Board
  • 5
    • 0035424364 scopus 로고    scopus 로고
    • Combined word-length optimization and highlevel synthesis of digital signal processing systems
    • Aug
    • K.-I. Kum and W. Sung, "Combined word-length optimization and highlevel synthesis of digital signal processing systems," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 20, no. 8, pp. 921-930, Aug. 2001.
    • (2001) IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. , vol.20 , Issue.8 , pp. 921-930
    • Kum, K.-I.1    Sung, W.2
  • 7
    • 2442598143 scopus 로고    scopus 로고
    • FPGAs vs. CPUs: Trends in peak floating-point performance
    • K. Underwood, "FPGAs vs. CPUs: Trends in peak floating-point performance," in Proc. Int. Symp. Field-Program. Gate Arrays, 2004, pp. 171-180.
    • (2004) Proc. Int. Symp. Field-Program. Gate Arrays , pp. 171-180
    • Underwood, K.1
  • 11
    • 70350068407 scopus 로고    scopus 로고
    • Finite precision bit-width allocation using SAT-modulo theory
    • A. B. Kinsman and N. Nicolici, "Finite precision bit-width allocation using SAT-modulo theory," in Proc. Int. Conf. DATE, 2009, pp. 1106-1111.
    • (2009) Proc. Int. Conf. DATE , pp. 1106-1111
    • Kinsman, A.B.1    Nicolici, N.2
  • 12
    • 77649154762 scopus 로고    scopus 로고
    • Bit-width allocation for hardware accelerators for scientific computing using SAT-modulo theory
    • Mar.
    • A. B. Kinsman and N. Nicolici, "Bit-width allocation for hardware accelerators for scientific computing using SAT-modulo theory," IEEE Trans. Comp.-Aided Des. Integr. Ciruits Sys., vol. 29, no. 3, pp. 405-413, Mar. 2010.
    • (2010) IEEE Trans. Comp.-Aided Des. Integr. Ciruits Sys. , vol.29 , Issue.3 , pp. 405-413
    • Kinsman, A.B.1    Nicolici, N.2
  • 13
    • 77956204830 scopus 로고    scopus 로고
    • Robust design methods for hardware accelerators for iterative algorithms in scientific computing
    • A. B. Kinsman and N. Nicolici, "Robust design methods for hardware accelerators for iterative algorithms in scientific computing," in Proc. Des. Automat. Conf., 2010, pp. 254-257.
    • Proc. Des. Automat. Conf. , vol.2010 , pp. 254-257
    • Kinsman, A.B.1    Nicolici, N.2
  • 17
    • 0028737371 scopus 로고
    • Search-based wordlength optimization for VLSI/DSP synthesis
    • H. Choi and W. Burleson, "Search-based wordlength optimization for VLSI/DSP synthesis," in Proc. Workshop VLSI Signal Process. VII, 1994, pp. 198-207.
    • (1994) Proc. Workshop VLSI Signal Process , vol.7 , pp. 198-207
    • Choi, H.1    Burleson, W.2
  • 18
    • 77954284922 scopus 로고    scopus 로고
    • Precision modeling and bit-width optimization of floating-point applications
    • Sep
    • Z. Zhao and M. Leeser, "Precision modeling and bit-width optimization of floating-point applications," in Proc. High Performance Embedded Comput., Sep. 2003, pp. 141-142.
    • (2003) Proc. High Performance Embedded Comput. , pp. 141-142
    • Zhao, Z.1    Leeser, M.2
  • 19
    • 0026169919 scopus 로고
    • Algorithms for arbitrary precision floating point arithmetic
    • Jun
    • D. Priest, "Algorithms for arbitrary precision floating point arithmetic," in Proc. IEEE. Symp. Comput. Arithmet., Jun. 1991, pp. 132-143.
    • (1991) Proc. IEEE. Symp. Comput. Arithmet. , pp. 132-143
    • Priest, D.1
  • 20
    • 0004293209 scopus 로고
    • Englewood Cliff, NJ: Prentice-Hall
    • R. E. Moore, Interval Analysis. Englewood Cliff, NJ: Prentice-Hall, 1966.
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 23
    • 0003088011 scopus 로고    scopus 로고
    • Computation and application of Taylor polynomials with interval remainder bounds
    • Jul
    • M. Berz and G. Hoffstätter, "Computation and application of Taylor polynomials with interval remainder bounds," Reliable Comput., vol. 4, pp. 83-97, Jul. 1998.
    • (1998) Reliable Comput. , vol.4 , pp. 83-97
    • Berz, M.1    Hoffstätter, G.2
  • 24
    • 0041573372 scopus 로고    scopus 로고
    • On the Lagrange remainder of the Taylor formula
    • U. Abel, "On the Lagrange remainder of the Taylor formula," Am. Math. Monthly, vol. 110, no. 7, pp. 627-633, 2003.
    • (2003) Am. Math. Monthly , vol.110 , Issue.7 , pp. 627-633
    • Abel, U.1
  • 25
    • 76249128779 scopus 로고    scopus 로고
    • Certification of bounds on expressions involving rounded operators
    • M. Daumas and G. Melquiond, "Certification of bounds on expressions involving rounded operators," ACM Trans. Math. Softw., vol. 37, no. 1, pp. 1-20, 2010.
    • (2010) ACM Trans. Math. Softw. , vol.37 , Issue.1 , pp. 1-20
    • Daumas, M.1    Melquiond, G.2
  • 26
    • 10044296444 scopus 로고    scopus 로고
    • Affine arithmetic: Concepts and applications
    • J. de Figueiredo and L. H. Stolfi, "Affine arithmetic: Concepts and applications," Numeric. Algorithms, vol. 37, no. 1, pp. 147-158, 2004.
    • (2004) Numeric. Algorithms , vol.37 , Issue.1 , pp. 147-158
    • De Figueiredo, J.1    Stolfi, L.H.2
  • 27
    • 77957986930 scopus 로고    scopus 로고
    • Tradeoff between approximation accuracy and complexity for range analysis using affine arithmetic
    • Apr
    • W. Z. L. Zhang and Y. Zhang, "Tradeoff between approximation accuracy and complexity for range analysis using affine arithmetic," J. Signal Process. Syst., vol. 61, pp. 279-291, Apr. 2010.
    • J. Signal Process. Syst. , vol.61 , Issue.2010 , pp. 279-291
    • Zhang, W.Z.L.1    Zhang, Y.2
  • 29
    • 0003571608 scopus 로고    scopus 로고
    • (Series Monographs and Textbooks in Pure and Applied Mathematics), New York: Marcel Dekker
    • E. Hansen and G. W. Walster, Global Optimization Using Interval Analysis (Series Monographs and Textbooks in Pure and Applied Mathematics), vol. 264. New York: Marcel Dekker, 2004.
    • (2004) Global Optimization Using Interval Analysis , vol.264
    • Hansen, E.1    Walster, G.W.2
  • 32
    • 80054827731 scopus 로고    scopus 로고
    • Rigorous affine lower bound functions for multivariate polynomials and their use in global optimisation
    • Sep
    • J. Garloff and A. P. Smith, "Rigorous affine lower bound functions for multivariate polynomials and their use in global optimisation," in Proc. Int. Conf. Appl. Oper. Res., vol. 1, no. 1. Sep. 2008, pp. 199-211.
    • (2008) Proc. Int. Conf. Appl. Oper. Res. , vol.1 , Issue.1 , pp. 199-211
    • Garloff, J.1    Smith, A.P.2
  • 33
    • 84972584455 scopus 로고
    • Representing polynomials by positive linear functions on compact convex polyhedra
    • D. Handelman, "Representing polynomials by positive linear functions on compact convex polyhedra," Pacific J. Math, vol. 132, no. 1, pp. 35-62, 1988.
    • (1988) Pacific J. Math , vol.132 , Issue.1 , pp. 35-62
    • Handelman, D.1
  • 34
    • 18744415993 scopus 로고    scopus 로고
    • Polynomial programming: LP-relaxations also converge
    • J. B. Lasserre, "Polynomial programming: LP-relaxations also converge," SIAM J. Optimiz., vol. 15, no. 2, pp. 383-393, 2005.
    • (2005) SIAM J. Optimiz. , vol.15 , Issue.2 , pp. 383-393
    • Lasserre, J.B.1
  • 35
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • Dec
    • M. R. Hestenes and E. Stiefel, "Methods of conjugate gradients for solving linear systems," J. Res. Nat. Bureau Standards, vol. 49, pp. 409-436, Dec. 1952.
    • (1952) J. Res. Nat. Bureau Standards , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 36
    • 34547422405 scopus 로고    scopus 로고
    • MPFR: A multiple-precision binary floating-point library with correct rounding
    • Jun
    • L. Fousse, G. Hanrot, V. Lefévre, P. Pélissier, and P. Zimmermann, "MPFR: A multiple-precision binary floating-point library with correct rounding," ACM Trans. Math. Softw., vol. 33, no. 2, pp. 1-14, Jun. 2007.
    • (2007) ACM Trans. Math. Softw. , vol.33 , Issue.2 , pp. 1-14
    • Fousse, L.1    Hanrot, G.2    Lefévre, V.3    Pélissier, P.4    Zimmermann, P.5
  • 37
    • 80054811664 scopus 로고    scopus 로고
    • Xilinx Corporation., Sep. [Online]. Available
    • Xilinx Corporation. (2010, Sep.). Core Generator Overview [Online]. Available: http://www.xilinx.com/itp/xilinx6/books/docs/cgn/cgn.pdf
    • (2010) Core Generator Overview
  • 38
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • P. A. Parrilo, "Semidefinite programming relaxations for semialgebraic problems," Math. Program. Ser. B, vol. 96, nos. 2-3, pp. 293-320, 2003.
    • (2003) Math. Program. Ser. B , vol.96 , Issue.2-3 , pp. 293-320
    • Parrilo, P.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.