Publications

Theory of the exact test of goodness of fit. British War Office, S.R.T.U. Report (1950) (with G. H. FREEMAN)

Computational method used in applying the exact test of goodness of fit. British War Office, S.R.T.U. Report (1950) (with G. H. FREEMAN)

Note on an exact treatment of contingency, goodness of fit, and other problems of significance. Biometrika, 38 (1951) pp. 141–149 (with G. H. FREEMAN)

Derivation of the hydrodynamic and thermodynamic equations of viscous flow in vector form, and their expression in general curvilinear coordinates. English Electric Co., Mechanical Engineering Laboratory Report (1956) 15 pp.

A bibliography of lubrication. English Electric Co., Mechanical Engineering Laboratory Report (1956)

The assumptions underlying Reynolds’ theory of hydrodynamic lubrication. English Electric Co., Mechanical Engineering Laboratory Report (1956)

The lubrication of plain bearings: an examination of Reynolds’ hydrodynamic theory. Distributed by Engineering (1956) 46 pp.

A method for increasing the efficiency of Monte Carlo integration. Journal of the Association for Computing Machinery, 4 (1957) pp. 329–340 (with D. C. HANDSCOMB)

Lubrication of plain bearings—Applicability of Reynolds’s hydrodynamic theory. Engineering (11 July 1958) pp. 59–60.

Elliptical whirl of flooded journal bearings. Proceedings of the Cambridge Philosophical Society, 54 (1958) pp. 119–127.

The shortest path through many points. Proceedings of the Cambridge Philosophical Society, 55 (1959) pp. 299–327 (with J. E. BEARDWOOD and J. M. HAMMERSLEY)

On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2 (1960) pp. 84–90.

The ‘FOGSTEP’ Fox-Goodwin integration routine. Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 16 (1961) 11 pp.

The extraction of reduced widths from (d, p) angular distributions. Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 20 (1961) 33 pp. (with P. E. HODGSON)

Four least-squares fitting programmes. Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 23 (1962) 33 pp.

Short programmes for the Mercury computer. Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 24 (1962) 15 pp.

‘HALTON. (D, P) STRIPPING. LN = 0.’ Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 25 (1962) 35 pp.

The ‘HALTON. (D, P) STRIPPING. LN = 0.’ programme. Oxford University, Clarendon Laboratory, Nuclear Physics Computing Group, Report No. 25A (1962) 70 pp.

Sequential Monte Carlo. Proceedings of the Cambridge Philosophical Society, 58 (1962) pp. 57–78.

Some divisibility properties of Fibonacci numbers. University of Colorado, Institute of Computer Science Report (1963) 14 pp.

G. E. Uhlenbeck, P. C. Hemmer, M. Kac. On the van der Waals theory of the vapor-liquid equilibrium. II. Discussion of the distribution functions. Journal of Mathematical Physics, 4 (1963), pp. 229–247. Appendix D—Proof of the identity (87), by J. H. Halton, pp. 246–247.

On the existence of square Fibonacci numbers. University of Colorado, Institute of Computer Science Report (1963) 12 pp.

A mathematical model of the effect of radiation on cells and cell colonies. RAND Corporation Report (1963) 15 pp.

The irrotational solution of an elliptic differential equation with an unknown coefficient. Brookhaven National Laboratory, Applied Mathematics Department Report No. 318, BNL 6909 (1963); Proceedings of the Cambridge Philosophical Society, 59 (1963) pp. 680–682 (with J. R. CANNON)

On the generation of an arbitrarily autocorrelated sequence of random variables from a sequence of independent random numbers. Brookhaven National Laboratory, Applied Mathematics Department Report No. 322, BNL 7299 (1963) 18 pp.

The distribution of the sequence {nξ} (n = 0, 1, 2, . . . ) University of Colorado, Institute of Computer Science Report (1964) 17 pp.

An interpretation of negative and other unorthodox probabilities. Brookhaven National Laboratory, Applied Mathematics Department Report No. 357, BNL 8429 (1964) 7 pp.

On Fibonacci residues. Fibonacci Quarterly, 2 (1964) pp. 217–218.

Algorithm 247: radical-inverse quasi-random point sequence [G5]. Communications of the Association for Computing Machinery, 7 (1964) pp. 701–702 (with G. B. SMITH)

On the relative merits of correlated and importance sampling for Monte Carlo integration. Brookhaven National Laboratory, Applied Mathematics Department Report No. 358, BNL 8428 (1964); Proceedings of the Cambridge Philosophical Society, 61 (1965) pp. 497–498.

A rigorous derivation of the exact contingency formula. Brookhaven National Laboratory, Applied Mathematics Department Report No. 369, BNL 8830 (1965) 7 pp.

On the generation of random sequences in Fréchet space. Brookhaven National Laboratory, Applied Mathematics Department Report No. 374, BNL 8996 (1965) 10 pp.

A note on Fibonacci subsequences. Brookhaven National Laboratory, Applied Mathematics Department Report No. 373, BNL 8997 (1965); Fibonacci Quarterly, 3 (1965) pp. 321–322.

A general formulation of the Monte Carlo method and a ‘strong law’ for certain sequential schemes. Brookhaven National Laboratory, Applied Mathematics Department Report No. 378, BNL 9220 (1965) 14 pp.

The statistics of signal detection for the differentially coherent phase shift keying system in non-Gaussian noise. Brookhaven National Laboratory, Applied Mathematics Department Report No. 385, BNL 9473 (1965) 19 pp.

Least-squares Monte Carlo methods for solving linear systems of equations. Brookhaven National Laboratory, Applied Mathematics Department Report No. 388, BNL 9678 (1965) 74 pp.

On a general Fibonacci identity. Fibonacci Quarterly, 3 (1965) pp. 31–43.

The distribution of the sequence {nξ} (n = 0, 1, 2, . . . ) Proceedings of the Cambridge Philosophical Society, 61 (1965) pp. 665–670.

An interpretation of negative probabilities. Proceedings of the Cambridge Philosophical Society, 62 (1966) pp. 83–86.

A combinatorial proof of a theorem of Tutte. Brookhaven National Laboratory, Applied Mathematics Department Report No. 391, BNL 9746 (1965); Proceedings of the Cambridge Philosophical Society, 62 (1966) pp. 683–684.

A combinatorial proof of Cayley’s theorem on Pfaffians. Brookhaven National Laboratory, Applied Mathematics Department Report No. 395, BNL 9818 (1965); Journal of Combinatorial Theory, 1 (1966) pp. 224–232.

Error rates in differentially coherent phase systems in non-Gaussian noise. Transactions of the Institute of Electrical and Electronic Engineers (Communications Technology), COM–14 (1966) pp. 594–601 (with A. D. SPAULDING)

An identity of the Jacobi type for Pfaffians. Brookhaven National Laboratory, Applied Mathematics Department Report No. 392, BNL 9757 (1965); Journal of Combinatorial Theory, 1 (1966) pp. 333–337.

Some properties associated with square Fibonacci numbers. Brookhaven National Laboratory, Applied Mathematics Department Report No. 384, BNL 9300 (1965); Fibonacci Quarterly, 5 (1967) pp. 347–355.

On the strong convergence of linear averages. University of Wisconsin, Madison, Mathematics Research Center Technical Summary Report No. 719 (1966) 8 pp.

On the divisibility properties of Fibonacci numbers. Fibonacci Quarterly, 4 (1966) pp. 217–240.

Sequential Monte Carlo (Revised). University of Wisconsin, Madison, Mathematics Research Center Technical Summary Report No. 816 (1967) 38 pp.

A rigorous derivation of the exact contingency formula. Proceedings of the Cambridge Philosophical Society, 65 (1969) pp. 527–530.

The extreme and L2 discrepancies of some plane sets. Monatshefte für Mathematik, 73 (1969) pp. 316–328 (with S. K. ZAREMBA)

Asymptotics for formula manipulation. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 54 (1969); Proceedings of the 1968 Summer Institute on Symbolic Mathematical Computation (I.B.M., Boston, 1969) pp. 149–194.

Proofs of algorithms for asymptotic series. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 54A (1969) 50 pp. (with R. L. LONDON)

Monte Carlo integration with sequential stratification. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 61 (1969) 31 pp. (with E. A. ZEIDMAN)

A retrospective and prospective survey of the Monte Carlo method. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 13 (1968); Society for Industrial and Applied Mathematics (SIAM) Review, 12 (1970) pp. 1–63.

The evaluation of multidimensional integrals by the Monte Carlo sequential stratification technique. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 137 (1971) 158 pp. (with E. A. ZEIDMAN)

Estimating the accuracy of quasi-Monte-Carlo integration. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 139 (1971); Applications of Number Theory to Numerical Analysis (Editor, S. K. ZAREMBA; Academic Press, New York, 1972) pp. 345–360.

On an algebraic identity with applications to operator theory. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 150 (1972) 29 pp. (with J. D. PINCUS)

Statistics of trees. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 334 (1978) 50 pp.

An almost surely optimal algorithm for the Euclidean Traveling Salesman Problem. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 335 (1978) 60 pp. (with R. TERADA)

An explicit formulation of the generalized antithetic transformation for Monte Carlo integration. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 348 (1979) 5 pp.

Foundations of Mathematical Analysis. §1: Sets and propositions; §2: Products, Relations, and Functions. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 381 (1980) 28 pp.

A fast algorithm for the Euclidean Traveling Salesman Problem, optimal with probability one. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 401 (1980) 30 pp. (with R. TERADA)

Generalized antithetic transformations for Monte Carlo sampling. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 408 (1980) 39 pp.

A co-factor identity for compound matrices. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 413 (1981) 8 pp.

Some elementary integrals in k-dimensional Euclidean space. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 416 (1981) 10 pp.

Multivariate regression analysis. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 425 (1981) 68 pp.

Using statistical techniques to find predictive relationships between variables. University of Wisconsin, Madison, Computer Sciences Department Technical Report No. 428 (1981) 19 pp.

Minimum variance Monte Carlo importance sampling with parametric dependence. Atomkernenergie–Kerntechnik, 37 (1981) pp. 188–193 (with C. W. MAYNARD and M. M. H. RAGHEB)

A fast algorithm for the Euclidean Traveling Salesman Problem, optimal with probability one. SIAM Journal on Computing, 11 (1982) pp. 28–46 (with R. TERADA)

The second industrial revolution. Wisconsin Medical Journal, 81: 4 (1982) pp. 40–42.

The anatomy of a computer. Wisconsin Medical Journal, 81: 5 (1982) pp. 16–18.

Communicating with the computer. Wisconsin Medical Journal, 81: 6 (1982) pp. 12–14.

Computer languages. Wisconsin Medical Journal, 81: 11 (1982) pp. 6–10.

Higher level languages. Wisconsin Medical Journal, 82: 2 (1983) pp. 31–34.

Computer software. Wisconsin Medical Journal, 84: 4 (1983) pp. 13–16.

Triangulation algorithms for simple, closed, not necessarily convex polygons in the plane. Harris Corporation, Government Systems Sector, Advanced Technology Department Technical Report (1984) 36 pp.

The ‘MPIA’ multiple precision interval arithmetic package. Harris Corporation, Government Systems Sector, Advanced Technology Department Technical Report (1984) 45 pp.

On the partitioning of programs on multi-computers. Harris Corporation, Government Systems Sector, Advanced Technology Department Technical Report (1984) 15 pp.

Tracing the exit edge from a cylindrically symmetric region with convex polygonal cross-section. University of California, Lawrence Livermore National Laboratory Working Paper (1984) 13 pp.

Triangulation algorithms for simple, closed, not necessarily convex polygons in the plane. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 85–008 (1985) 84 pp.

On the effect of selective sterilization on sex-ratio. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 85–019 (1985) 20 pp.

Triangulation algorithms for simple, closed, not necessarily convex polygons in the plane, II. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 85–024 (1985) 45 pp.

The anatomy of computing. The Information Technology Revolution (Editor, T. FORESTER; M.I.T. Press, Cambridge, Massachusetts, 1985) pp. 3–26.

A Mini-Course on Probability and Statistics (University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 85–032; Thistle Press, 1985) 108 pp.

Two algebraic problems. SIAM Review, 28 (1986) pp. 231–232.

Topics in Numerical Methods (Thistle Press, 1982; Fifth Edition, 1987) 329 pp.

On the efficiency of generalized antithetic transformations for Monte Carlo integration. Nuclear Science and Engineering, 98 (1988) pp. 299–316.

Monte Carlo anti-aliasing. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 88–018 (1988) 8 pp.

On the random covering problem. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 88–034 (1988) 31 pp.

On a new class of independent families of linear congruential pseudo-random sequences. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 87–001 (1987) 22 pp. Accepted for presentation at Twelfth IMACS World Congress on Scientific Computation, Paris, France, July 1988.

Tree-structured pseudo-random sequences. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 88–003 (1988) 84 pp.

The properties of random trees. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 86–024 (1986); Information Sciences, 47 (1989) pp. 95–133.

On the geometry of a general three-camera headmounted system. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 89–019 (1989) 44 pp.

Pseudo-random trees—multiple independent sequence generators for parallel and branching computations. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 88–037 (1988); Journal of Computational Physics, 84 (1989) pp. 1–56.

Pseudo-random trees. 23 pp. Invited presentation at NSF–CBMS Research Conference on Random Number Generation and Quasi-Monte-Carlo Methods, Fairbanks, Alaska, August 1990.

Monte Carlo methods for solving linear systems of equations. 18 pp. Invited presentation at NSF–CBMS Research Conference on Random Number Generation and Quasi-Monte-Carlo Methods, Fairbanks, Alaska, August 1990.

On the thickness of graphs of given degree. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 87–025 (1987) 22 pp.; Information Sciences, 54 (1991) pp. 219–238.

Introduction to Computers—Course Book (Thistle press, 1988; Sixth Edition, 1991) 211 pp.

Random sequences in Fréchet spaces. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 89–038 (1989) 24 pp.; Journal of Scientific Computing, 6 (1991) pp. 61–77.

Random sequences in generalized Cantor sets. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 90–020 (1990) 12 pp.; Journal of Scientific Computing, 6 (1991) pp. 415–423.

Simplicial multivariable linear interpolation. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 91–002 (1991) 15 pp.

An introduction to the Monte Carlo solution of linear systems. 18 pp. Invited presentation at IMACS International Symposium on Iterative Methods in Linear Algebra, Brussels, Belgium, April 1991.

Some new results on the Monte Carlo solution of linear systems, including sequential methods. 20 pp. Invited presentation at IMACS International Symposium on Iterative Methods in Linear Algebra, Brussels, Belgium, April 1991.

Reject the rejection technique. University of North Carolina at Chapel Hill, Department of Computer Science Technical Note (1989) 10 pp.; Journal of Scientific Computing, 7 (1992) pp. 281–287.

The Monte Carlo solution of linear systems. University of North Carolina at Chapel Hill, Working Paper (1991) 132 pp.; reprinted in Readings on the Monte Carlo Method, John H. Halton (1992) 404 pp.

Sequential Monte Carlo techniques for the solution of linear systems. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 92–033 (1992) 46 pp.

Geometry of a three-camera headmounted system. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 93–022 (1993) 26 pp.; Information Sciences, 77 (1994) pp. 51–75.

Sequential Monte Carlo techniques for the solution of linear systems. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 93–028 (1993) 49 pp.; Journal of Scientific Computing, 9 (1994) pp. 213–257.

The polydendron—A well-connected graph. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 94–007 (1994) 16 pp.

Sequential Monte Carlo techniques for the solution of linear systems. Journal of Scientific Computing, 9 (1994), pp. 213–257.

The Shoelace Problem. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 92–032 (1992) 19 pp. Mathematical Intelligencer, 17 (1995) , (4) pp. 36–41.

Scheduling mass oral examinations—a study in the power of randomization. Presented to University of North Carolina at Chapel Hill, Operations Research & Systems Analysis Colloquium, 12 Oct. 1995.

A property of certain squares. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 95–002 (1995) 19 pp.

Sequential Monte Carlo techniques for solving non-linear systems University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 96–042 (1995) 35 pp.; invited presentation at CNLS/LANL Workshop on Adaptive Monte Carlo Methods, Los Alamos, New Mexico, August 1996.

On accelerating Monte Carlo techniques for solving large systems of equations. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 96–041 (1996) 27 pp.

A very fast algorithm for finding eigenvalues and eigenvectors. University of North Carolina at Chapel Hill, Department of Computer Science Technical Report No. 96–043 (1996) 43 pp.

Increasing the efficiency of radiation shielding calculations by using antithetic variates. Invited presentation at IMACS Seminar on Monte Carlo Methods, Université Libre de Bruxelles, Brussels, Belgium, April 1997 35 pp.; Mathematics and Computers in Simulation, 47 (1998) pp. 309-318 (with P. K. SARKAR).

A rigorous justification for quasi-Monte-Carlo methods and valid statistical estimates of their accuracy. Invited presentation at Monte Carlo workshop, Stennis Space Center, 22–24 April, 1998.

Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically. Invited presentation at Wolfram Research Inc., Champaign, IL, 18 May, 1998.

Independence of quasi-random sequences and sets. Invited presentation at International Conference on Monte Carlo and Quasi-Monte-Carlo Methods, Claremont Graduate School, CA, 22–26 June 1998.

Asymptotic complexity of Monte Carlo methods for solving linear systems. Journal of Statistical Planning and Inference, 85 (2000) pp. 5–18 (with D. L. DANILOV and S. M. ERMAKOV).

Invited to confer on Monte Carlo methods for graphic rendering and to give two public lectures at Universitat di Girona, Girona, Spain, 25 May 2001–9 June 2001. (i) “Sequential Monte Carlo techniques for solving nonlinear problems” (Lluis Santalo Lecture on Applied Mathematics) and (ii) “Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically.”

Invited to participate in the Dagstuhl Seminar on Stochastic Methods in Rendering, Schloss Dagstuhl, Germany, 10–15 June 2001 and to give an invited lecture on “Why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically.”

Accelerating path-tracing by re-using paths. Rendering Techniques 2002 (Eurographics Workshop on Rendering). ACM Siggraph Press (2002) pp. 125–134 and p. 325 (with P. BEKAERT and M. SBERT).

Invited to attend the 4th IMACS Seminar on Monte Carlo Methods, 15-19 September 2003, sponsored by the Weierstrass Institute of Applied Analysis, the Konrad Zuse Center for Scientific Computing, and the Humboldt University, in Berlin, Germany, to give the opening plenary lecture there, on “Quasi-probability.”

Invited to attend the 7th Joint Conference on Information Sciences, 26–30 September 2003, in Research Triangle Park, Cary, NC, to speak on “A new approach to the rigorous validation of quasi-Monte-Carlo methods.” Proceedings of 7th JCIS (2003) p. 1758.

An outline of quasi-probability. Monte Carlo Methods & Applications, 10 (2004) pp. 183–196.

Reusing paths in radiosity and global illumination. Monte Carlo Methods & Applications 10 (2004) pp. 575–585 (with M. SBERT and P. BEKAERT).

A general estimator for Fredholm integral equations of the second kind. Universitat de Girona, Research Report (2004) 5 pp. (with M. SBERT and P. BEKAERT).

“Sequential Monte Carlo techniques for solving non-linear systems.” Invited presentation at Fifth IMACS Seminar on Monte Carlo Methods—MCM2005, Florida State University, Tallahassee, FL, May 2005. 26 pp.

Quasi-probability—why quasi-Monte-Carlo methods are statistically valid and how their errors can be estimated statistically. Monte Carlo Methods & Applications, 11 (2005) pp. 203–350.

Sequential Monte Carlo techniques for solving non-linear systems. Monte Carlo Methods & Applications, 12 (2006) pp. 113–141.

Fast GPU-based reuse of paths in radiosity. Monte Carlo Methods & Applications, 13 (2007) pp. 253–274 (with F. CASTRO, G. PATOW, and M. SBERT).

Efficient reuse of paths for random walk radiosity. Computers & Graphics, 32 (2008) pp. 65–81 (with F. CASTRO and M. SBERT).

Sequential Monte Carlo for linear systems—a practical summary. Monte Carlo Methods & Applications, 14 (2008) pp. 1–27.

Sigma-algebra theorems.  Monte Carlo Methods & Applications, 14 (2008) pp. 171–189.