Eldon Robert Hansen is an American mathematician and author who has published in global optimization theory and interval arithmetic.
Hansens's primary publications include Global Optimization Using Interval Analysis (1992), A Table of Series and Products (1975), and Topics in Interval Analysis (1969). He also co-authored a number of works with the mathematician William Walster.
Hansen taught at Stanford University, The University of California at Berkeley, San Jose State College, Oxford University, and Washington State University;
Hansen's algorithm extended the classical Gauss-Seidel algorithm to interval computations, and has been used to compute uncertainties in delta wing composite structures (Delcroix, Boyer, & Braibant)
Hansen's method used interval analysis to solve a supposedly "insoluble" global optimization problem. The method was originally described for both the one-dimensional and multi-dimensional cases in the 1980s, and is more fully described in the 1992 Global Optimization Using Interval Analysis and the 2nd edition of the book written with William Walster in 2003, and was translated into Russian in 2012.
Referencesedit
Bull. Amer. Math. Soc. (1961). American Doctorates Conferred in 1960 67 (3): 316–331.
Delcroix, F.; Boyer, C. & Braibant, V. Computing Uncertainties in a Delta Wing Composite Using Interval Based Methods
Gilliland, Dennis C.; Hansen, Eldon R. A note on some series representations of the integral of a bivariate normal distribution over an offset circle. Naval Res. Logist. Quart. 21 (1974), 207–211.
Hansen, E. Interval forms of Newton's method. Computing 20 (1978), no. 2, 153–163.
Hansen, E.; Patrick, M.; Rusnak, J. Some modifications of Laguerre's method. Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 4, 409–417.
Hansen, E. R. Bounding the set of solutions of a perturbed global optimization problem. 2nd IIASA Workshop on Global Optimization (Sopron, 1990). J. Global Optim. 1 (1991), no. 4, 359–374.
Hansen. E.R. Bounding the solution of interval linear equations. SIAM J. Numer. Anal. 29 (1992), no. 5, 1493–1503.
Hansen, E.R. Computing zeros of functions using generalized interval arithmetic. Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification (Lafayette, LA, 1993). Interval Comput./Interval. Vychisl. 1993, no. 3, 3--28.
Hansen, E. R. (1975). "A Generalized Interval Arithmetic," In: K. Nickel (ed.), Interval Mathematics, Springer-Verlag, Lecture Notes in Computer Science, Vol. 29, pp. 7–18.
Hansen, E. R. Global optimization using interval analysis: the one-dimensional case. J. Optim. Theory Appl. 29 (1979), no. 3, 331–344.
Hansen, E. R. Preconditioning linearized equations. Computing 58 (1997), no. 2, 187–196.
Hansen, E. R.; Greenberg, R. I. An interval Newton method. Appl. Math. Comput. 12 (1983), no. 2–3, 89–98.
Hansen, Eldon; Sengupta, Saumyendra. Bounding solutions of systems of equations using interval analysis. BIT 21 (1981), no. 2, 203–211.
Hansen, E.R.; Sengupta, S. (1983). "Summary and Steps of a Global Nonlinear Constrained Optimization Algorithm," Report D88977, Lockheed Missiles and Space Co.
Hansen, E. R.; Walster, G. W. Bounds for Lagrange multipliers and optimal points. Comput. Math. Appl. 25 (1993), no. 10–11, 59–69.
Hansen, Eldon. The centered form. In Topics in Interval analysis, Oxford Press, 1969, pp. 102–106.
Hansen, Eldon. Cyclic composite multistep predictor-corrector methods. Proc. 1969 ACM National Conference, 135–139.
Hansen, Eldon. A generalized interval arithmetic. In Interval Mathematics, K. Nickel., ed. Springer-Verlag, 1975, pp. 7–18.
Hansen, Eldon. Global optimization using interval analysis. Monographs and Textbooks in Pure and Applied Mathematics, 165. Marcel Dekker, Inc., New York, 1992. xvi+230 pp. ISBN0-8247-8696-3
Hansen, Eldon. Global optimization using interval analysis—the multidimensional case. Numer. Math. 34 (1980), no. 3, 247–270.
Hansen, Eldon. Global optimization with data perturbations. Comput. Oper. Res. 11 (1984), no. 2, 97–104.
Hansen, Eldon. A globally convergent interval method for computing and bounding real roots. BIT 18 (1978), no. 4, 415–424.
Hansen, Eldon R. The hull of preconditioned interval linear equations. Reliab. Comput. 6 (2000), no. 2, 95–103.
Hansen, Eldon. Interval arithmetic in matrix computations. I. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 1965 308–320.
Hansen, Eldon. On computing the exact characteristic polynomial. 17th national meeting of ACM, Digest of Technical Papers. 1962, pp. 104–105.
Hansen, Eldon. On linear algebraic equations with interval coefficients. In Topics in Interval analysis, Oxford Press, 1969, pp. 35–46.
Hansen, Eldon. On solving two-point boundary value problems using interval arithmetic. In Topics in Interval analysis, Oxford Press, 1969, pp. 74–90.
Hansen, Eldon. An overview of global optimization using interval analysis. Reliability in computing, 289–307, Perspect. Comput., 19, Academic Press, Boston, MA, 1988.
Hansen, Eldon; McNolty, Frank. Statistical distributions occurring in photoelectron phenomena, radar and infrared applications. In C. Taille et al. (eds.) Statistical distributions in scientific work, vol. 6, 47–77.
Hansen, Eldon; Rasmussen, J.G. Numerical solution of the Curium-242 alpha decay wave equation. Phys. Rev. 109(5) 1958 1656–1663.
Hansen, Eldon; Smith, Roberta. A computer program for solving a system of linear equations and matrix inversion with automatic error bounding using interval arithmetic. Technical report LMSC 4-22-66-3, Lockheed Missiles and Space Co., Palo Alto, CA, 1966.
Hansen, Eldon R. On the Danilewski method. Journal of the Association for Computing Machinery 10 1963 102–109.
Hansen, Eldon R. On quasicyclic Jacobi methods. Journal of the Association for Computing Machinery 9 1962 118–135.
Hansen, Eldon R. On solving systems of equations using interval arithmetic. Math. Comp. 22 1968 374–384.
Hansen, Eldon. On some sums and integrals involving Bessel functions. Amer. Math. Monthly 73 1966 143–150.
Hansen, Eldon. On the solution of linear algebraic equations with interval coefficients. Linear Algebra and Appl. 2 1969, 153–165.
Hansen, Eldon; Clow, R.; McNolty, Frank. Bayesian Density Functions for Gaussian Noise. Proc. IEEE, 62 (1974), 4134–136.
Hansen, Eldon; Clow, R; McNolty, Frank. Detection probabilities for fluctuating infrared targets, J. Appl. Optics, 14 (1975), 61–66.
Hansen, Eldon; Clow, R.; McNolty, Frank. Some properties of the output integrator in an infrared system. IEEE Trans. Aero. Elect. Sys., AES-8 (1972), 428–438.
Hansen, Eldon; Gilliliand, D. On a series representations of the integral of a bivariate normal distribution over an offset circle. Dept. of Stat. & Prob., Michigan State Univ., RM247, DCG12, 1970.
Hansen, Eldon; Huynen, R.; McNolty, Frank. Certain statistical distributions involving special functions and their applications in Sstatistical distributions in scientific work, Vol. 1: Models and structures. G.P. Patil, S. Kotz, and J.K. Ord, eds., D. Reidel Publ. Co., 1975.
Hansen, Eldon; Oomen, B.J. The optimal properties of two action discretized linear reward-inaction learning automata. Proc. Computer and Info System Sciences Conf., Princeton Univ., March 15–16, 1984.
Hansen, Eldon; Patrick, Merrell. Estimating the multiplicity of a root. Numer. Math. 27 (1976/77), no. 1, 121–131.
Hansen, Eldon; Patrick, Merrell. A family of root finding methods. Numer. Math. 27 (1976/77), no. 3, 257–269
Hansen, Eldon R.; Patrick, Merell L.; Wang, Richard L. C. Polynomial evaluation with scaling. ACM Trans. Math. Software 16 (1990), no. 1, 86–93.
Hansen, Eldon; Sengupta, Saumyendra. Bounding solutions of systems of equations using interval analysis. BIT 21 (1981), no. 2, 203–211.
Hansen, Eldon; Sengupta, Saumyendra. Global constrained optimization using interval analysis. Interval mathematics, 1980 (Freiburg, 1980), pp. 25–47, Academic Press, New York-London, 1980.
Hansen, Eldon; Smith, Roberta. Interval arithmetic in matrix computations. II. SIAM J. Numer. Anal. 4 1967 1--9.
Hansen, Eldon; G. William Walster. global optimization in nonlinear mixed integer problems. In William F. Ames and R. Vichnevesky, eds. Proceedings of the 10th IMACS world congress on systems simulation and scientific computing, vol. 1. IMACS, Plantation, FL, 1982, pp. 379–381.
Hansen, Eldon; Walster, G. William. Global optimization using interval analysis. Second edition, revised and expanded. With a foreword by Ramon Moore. Monographs and Textbooks in Pure and Applied Mathematics, 264. Marcel Dekker, Inc., New York, 2004. xviii+489 pp.
Hansen, Eldon R. On computing the exact characteristic polynomial. 17th National Meeting of ACM, Digest of Technical Papers, 1962, pp. 265–104.
Hansen, Eldon R. On cyclic Jacobi methods. J. Soc. Indust. Appl. Math. 11 1963 448–459.
Hansen, Eldon. A multidimensional interval Newton method. Reliab. Comput. 12 (2006), no. 4, 253–272.
Hansen, Eldon R. Sharpness in interval computations. Reliab. Comput. 3 (1997), no. 1, 17–29.
Hansen, Eldon R. (1975). A Table of Series and Products. Upper Saddle River, NJ: Prentice-Hall.
Hansen, Eldon. A theorem on regularity of interval matrices. Reliab. Comput. 11 (2005), no. 6, 495–497.
Hansen, Eldon R. (1969). Topics in Interval Analysis. Oxford: Oxford UP.
Hansen, Eldon R., Comstock, R.L. Analysis of nondegenerate parallel pumping of magnetoelastic waves in ferrogmagnets. J. Applied Physics., 36 (1965), 1567-1569.
Hansen, Eldon R.; Patrick, Merrell L. Some relations and values for the generalized Riemann zeta functions. Math. Comp. 16 1962 265–274.
Hansen, Eldon R.; Walster, G. William. Sharp bounds on interval polynomial roots. Reliab. Comput. 8 (2002), no. 2, 115–122.
Hansen, Eldon; Walster, G. William. Solving overdetermined systems of interval linear equations. Reliab. Comput. 12 (2006), no. 3, 239–243.
Hansen, Eldon Robert. ON JACOBI METHODS AND BLOCK-JACOBI METHODS FOR COMPUTING MATRIX EIGENVALUES. Thesis (Ph.D.)–Stanford University. ProQuest LLC, Ann Arbor, MI, 1960. 129 pp.
Huynen, J. Richard; McNolty, Frank; Hansen, Eldon. Component distributions for fluctuating radar targets. IEEE Trans. Aerospace and Electron. Systems AES-11 (1975), no. 6, 1316–1332.
McNolty, Frank; Doyle, James; Hansen, Eldon. Properties of the mixed exponential failure process. Technometrics 22 (1980), no. 4, 555–565.
McNolty, Frank; Hansen, Eldon. Some aspects of Swerling models for fluctuating radar cross section. IEEE Trans. Aerospace and Electron. Systems AES-10 (1974), 281–285.
Oommen, B. J.; Hansen, Eldon. The asymptotic optimality of discretized linear reward-inaction learning automata. IEEE Trans. Systems Man Cybernet. 14 (1984), no. 3, 542–545.
Oommen, B. John; Hansen, E. R. List organizing strategies using stochastic move-to-front and stochastic move-to-rear operations. SIAM J. Comput. 16 (1987), no. 4, 705–716.
Oommen, B. John; Hansen, E. R.; Munro, J. I. Deterministic optimal and expedient move-to-rear list organizing strategies. Theoret. Comput. Sci. 74 (1990), no. 2, 183–197.
Walster, G. William; Hansen, Eldon R. Computing interval parameter bounds from fallible measurements using overdetermined (tall) systems of nonlinear equations. COCOS 2002. 171-177.
Walster, G. William; Hansen, Eldon. Using pillow functions to efficiently compute crude range tests. Numer. Algorithms 37 (2004), no. 1-4, 401–415.
Walster, G. W.; Hansen, E. R.; Sengupta, S. Test results for a global optimization algorithm. Numerical optimization, 1984 (Boulder, Colo., 1984), 272–287, SIAM, Philadelphia, PA, 1985.
April 12, 2024
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This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations February 2014 Learn how and when to remove this template message This biography of a living person needs additional citations for verification Please help by adding reliable sources Contentious material about living persons that is unsourced or poorly sourced must be removed immediately from the article and its talk page especially if potentially libelous Find sources Eldon Hansen news newspapers books scholar JSTOR January 2020 Learn how and when to remove this template message A major contributor to this article appears to have a close connection with its subject It may require cleanup to comply with Wikipedia s content policies particularly neutral point of view Please discuss further on the talk page January 2020 Learn how and when to remove this template message This article has an unclear citation style The references used may be made clearer with a different or consistent style of citation and footnoting December 2020 Learn how and when to remove this template message Learn how and when to remove this template message Eldon Robert Hansen is an American mathematician and author who has published in global optimization theory and interval arithmetic Hansens s primary publications include Global Optimization Using Interval Analysis 1992 A Table of Series and Products 1975 and Topics in Interval Analysis 1969 He also co authored a number of works with the mathematician William Walster Contents 1 Background 2 Research 3 References 4 BibliographyBackground editHe was born in 1927 near Rochester Washington He completed his undergraduate studies at the University of California Berkeley Hansen received his Ph D in mathematics from Stanford University in 1960 on Jacobi methods and Block Jacobi methods for computing matrix eigenvalues Bulletin of the American Mathematical Society 1961 Hansen taught at Stanford University The University of California at Berkeley San Jose State College Oxford University and Washington State University Hansen also worked at Lockheed Corporation in Palo Alto California Research editHansen s algorithm extended the classical Gauss Seidel algorithm to interval computations and has been used to compute uncertainties in delta wing composite structures Delcroix Boyer amp Braibant Hansen s method used interval analysis to solve a supposedly insoluble global optimization problem The method was originally described for both the one dimensional and multi dimensional cases in the 1980s and is more fully described in the 1992 Global Optimization Using Interval Analysis and the 2nd edition of the book written with William Walster in 2003 and was translated into Russian in 2012 References editBull Amer Math Soc 1961 American Doctorates Conferred in 1960 67 3 316 331 Delcroix F Boyer C amp Braibant V Computing Uncertainties in a Delta Wing Composite Using Interval Based MethodsBibliography editDonelson John III Hansen Eldon Cyclic composite multistep predictor corrector methods SIAM J Numer Anal 8 1971 137 157 Gilliland Dennis C Hansen Eldon R A note on some series representations of the integral of a bivariate normal distribution over an offset circle Naval Res Logist Quart 21 1974 207 211 Hansen E Interval forms of Newton s method Computing 20 1978 no 2 153 163 Hansen E Patrick M Rusnak J Some modifications of Laguerre s method Nordisk Tidskr Informationsbehandling BIT 17 1977 no 4 409 417 Hansen E R Bounding the set of solutions of a perturbed global optimization problem 2nd IIASA Workshop on Global Optimization Sopron 1990 J Global Optim 1 1991 no 4 359 374 Hansen E R Bounding the solution of interval linear equations SIAM J Numer Anal 29 1992 no 5 1493 1503 Hansen E R Computing zeros of functions using generalized interval arithmetic Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification Lafayette LA 1993 Interval Comput Interval Vychisl 1993 no 3 3 28 Hansen E R 1975 A Generalized Interval Arithmetic In K Nickel ed Interval Mathematics Springer Verlag Lecture Notes in Computer Science Vol 29 pp 7 18 Hansen E R Global optimization using interval analysis the one dimensional case J Optim Theory Appl 29 1979 no 3 331 344 Hansen E R Preconditioning linearized equations Computing 58 1997 no 2 187 196 Hansen E R Greenberg R I An interval Newton method Appl Math Comput 12 1983 no 2 3 89 98 Hansen Eldon Sengupta Saumyendra Bounding solutions of systems of equations using interval analysis BIT 21 1981 no 2 203 211 Hansen E R Sengupta S 1983 Summary and Steps of a Global Nonlinear Constrained Optimization Algorithm Report D88977 Lockheed Missiles and Space Co Hansen E R Walster G W Bounds for Lagrange multipliers and optimal points Comput Math Appl 25 1993 no 10 11 59 69 Hansen Eldon The centered form In Topics in Interval analysis Oxford Press 1969 pp 102 106 Hansen Eldon Cyclic composite multistep predictor corrector methods Proc 1969 ACM National Conference 135 139 Hansen Eldon A generalized interval arithmetic In Interval Mathematics K Nickel ed Springer Verlag 1975 pp 7 18 Hansen Eldon Global optimization using interval analysis Monographs and Textbooks in Pure and Applied Mathematics 165 Marcel Dekker Inc New York 1992 xvi 230 pp ISBN 0 8247 8696 3 Hansen Eldon Global optimization using interval analysis the multidimensional case Numer Math 34 1980 no 3 247 270 Hansen Eldon Global optimization with data perturbations Comput Oper Res 11 1984 no 2 97 104 Hansen Eldon A globally convergent interval method for computing and bounding real roots BIT 18 1978 no 4 415 424 Hansen Eldon R The hull of preconditioned interval linear equations Reliab Comput 6 2000 no 2 95 103 Hansen Eldon Interval arithmetic in matrix computations I J Soc Indust Appl Math Ser B Numer Anal 2 1965 308 320 Hansen Eldon On computing the exact characteristic polynomial 17th national meeting of ACM Digest of Technical Papers 1962 pp 104 105 Hansen Eldon On linear algebraic equations with interval coefficients In Topics in Interval analysis Oxford Press 1969 pp 35 46 Hansen Eldon On solving two point boundary value problems using interval arithmetic In Topics in Interval analysis Oxford Press 1969 pp 74 90 Hansen Eldon An overview of global optimization using interval analysis Reliability in computing 289 307 Perspect Comput 19 Academic Press Boston MA 1988 Hansen Eldon Sums of functions satisfying recursion relations Amer Math Monthly 88 1981 no 9 676 679 Hansen Eldon McNolty Frank Statistical distributions occurring in photoelectron phenomena radar and infrared applications In C Taille et al eds Statistical distributions in scientific work vol 6 47 77 Hansen Eldon Rasmussen J G Numerical solution of the Curium 242 alpha decay wave equation Phys Rev 109 5 1958 1656 1663 Hansen Eldon Smith Roberta A computer program for solving a system of linear equations and matrix inversion with automatic error bounding using interval arithmetic Technical report LMSC 4 22 66 3 Lockheed Missiles and Space Co Palo Alto CA 1966 Hansen Eldon R On the Danilewski method Journal of the Association for Computing Machinery 10 1963 102 109 Hansen Eldon R On quasicyclic Jacobi methods Journal of the Association for Computing Machinery 9 1962 118 135 Hansen Eldon R On solving systems of equations using interval arithmetic Math Comp 22 1968 374 384 Hansen Eldon On some sums and integrals involving Bessel functions Amer Math Monthly 73 1966 143 150 Hansen Eldon On the solution of linear algebraic equations with interval coefficients Linear Algebra and Appl 2 1969 153 165 Hansen Eldon Clow R McNolty Frank Bayesian Density Functions for Gaussian Noise Proc IEEE 62 1974 4134 136 Hansen Eldon Clow R McNolty Frank Detection probabilities for fluctuating infrared targets J Appl Optics 14 1975 61 66 Hansen Eldon Clow R McNolty Frank Some matched filter configurations for infrared systems IEEE Trans Aero Elect Sys AES 8 1972 552 558 Hansen Eldon Clow R McNolty Frank Some properties of the output integrator in an infrared system IEEE Trans Aero Elect Sys AES 8 1972 428 438 Hansen Eldon Gilliliand D On a series representations of the integral of a bivariate normal distribution over an offset circle Dept of Stat amp Prob Michigan State Univ RM247 DCG12 1970 Hansen Eldon Huynen R McNolty Frank Certain statistical distributions involving special functions and their applications in Sstatistical distributions in scientific work Vol 1 Models and structures G P Patil S Kotz and J K Ord eds D Reidel Publ Co 1975 Hansen Eldon Oomen B J The optimal properties of two action discretized linear reward inaction learning automata Proc Computer and Info System Sciences Conf Princeton Univ March 15 16 1984 Hansen Eldon Patrick Merrell Estimating the multiplicity of a root Numer Math 27 1976 77 no 1 121 131 Hansen Eldon Patrick Merrell A family of root finding methods Numer Math 27 1976 77 no 3 257 269 Hansen Eldon R Patrick Merell L Wang Richard L C Polynomial evaluation with scaling ACM Trans Math Software 16 1990 no 1 86 93 Hansen Eldon Sengupta Saumyendra Bounding solutions of systems of equations using interval analysis BIT 21 1981 no 2 203 211 Hansen Eldon Sengupta Saumyendra Global constrained optimization using interval analysis Interval mathematics 1980 Freiburg 1980 pp 25 47 Academic Press New York London 1980 Hansen Eldon Smith Roberta Interval arithmetic in matrix computations II SIAM J Numer Anal 4 1967 1 9 Hansen Eldon G William Walster global optimization in nonlinear mixed integer problems In William F Ames and R Vichnevesky eds Proceedings of the 10th IMACS world congress on systems simulation and scientific computing vol 1 IMACS Plantation FL 1982 pp 379 381 Hansen Eldon Walster G William Global optimization using interval analysis Second edition revised and expanded With a foreword by Ramon Moore Monographs and Textbooks in Pure and Applied Mathematics 264 Marcel Dekker Inc New York 2004 xviii 489 pp Hansen Eldon R On computing the exact characteristic polynomial 17th National Meeting of ACM Digest of Technical Papers 1962 pp 265 104 Hansen Eldon R On cyclic Jacobi methods J Soc Indust Appl Math 11 1963 448 459 Hansen Eldon A multidimensional interval Newton method Reliab Comput 12 2006 no 4 253 272 Hansen Eldon R Reminiscence Reliab Comput 6 2000 no 2 225 226 Hansen Eldon R On solving systems of equations using interval arithmetic Math Comp 22 1968 374 384 Hansen Eldon Sharpening interval computations Reliab Comput 12 2006 no 1 21 34 Hansen Eldon R Sharpness in interval computations Reliab Comput 3 1997 no 1 17 29 Hansen Eldon R 1975 A Table of Series and Products Upper Saddle River NJ Prentice Hall Hansen Eldon A theorem on regularity of interval matrices Reliab Comput 11 2005 no 6 495 497 Hansen Eldon R 1969 Topics in Interval Analysis Oxford Oxford UP Hansen Eldon R Comstock R L Analysis of nondegenerate parallel pumping of magnetoelastic waves in ferrogmagnets J Applied Physics 36 1965 1567 1569 Hansen Eldon R Patrick Merrell L Some relations and values for the generalized Riemann zeta functions Math Comp 16 1962 265 274 Hansen Eldon R Walster G William Sharp bounds on interval polynomial roots Reliab Comput 8 2002 no 2 115 122 Hansen Eldon Walster G William Solving overdetermined systems of interval linear equations Reliab Comput 12 2006 no 3 239 243 Hansen Eldon Robert ON JACOBI METHODS AND BLOCK JACOBI METHODS FOR COMPUTING MATRIX EIGENVALUES Thesis Ph D Stanford University ProQuest LLC Ann Arbor MI 1960 129 pp Huynen J Richard McNolty Frank Hansen Eldon Component distributions for fluctuating radar targets IEEE Trans Aerospace and Electron Systems AES 11 1975 no 6 1316 1332 McNolty Frank Doyle James Hansen Eldon Properties of the mixed exponential failure process Technometrics 22 1980 no 4 555 565 McNolty Frank Hansen Eldon Some aspects of Swerling models for fluctuating radar cross section IEEE Trans Aerospace and Electron Systems AES 10 1974 281 285 Neumaier A 1980 Review Global Optimization Using Interval Analysis Available at https www mat univie ac at neum glopt hansen html Oommen B J Hansen Eldon The asymptotic optimality of discretized linear reward inaction learning automata IEEE Trans Systems Man Cybernet 14 1984 no 3 542 545 Oommen B John Hansen E R List organizing strategies using stochastic move to front and stochastic move to rear operations SIAM J Comput 16 1987 no 4 705 716 Oommen B John Hansen E R Munro J I Deterministic optimal and expedient move to rear list organizing strategies Theoret Comput Sci 74 1990 no 2 183 197 Walster G William Hansen Eldon R Computing interval parameter bounds from fallible measurements using overdetermined tall systems of nonlinear equations COCOS 2002 171 177 Walster G William Hansen Eldon Using pillow functions to efficiently compute crude range tests Numer Algorithms 37 2004 no 1 4 401 415 Walster G W Hansen E R Sengupta S Test results for a global optimization algorithm Numerical optimization 1984 Boulder Colo 1984 272 287 SIAM Philadelphia PA 1985 Retrieved from https en wikipedia org w index php title Eldon Hansen amp oldid 1185331750, wikipedia, wiki, book, books, library,
