James N. Lyness

PUBLICATIONS appearing in the open refereed scientific literature.

[1] J. N. Lyness, "Polarization in Nuclear Reactions," Proc. Phys.
Soc. 71 (1958) 858-860

[2] J. N. Lyness, "A Method for Calculating Scattering Phase Shifts,"
Nucl. Phys. 18 (1960) 654-668

[3] J. N. Lyness, and J. M. Blatt, "The Practical Use of Variation
Principles in the Determination of the Stability of Non-Linear
Systems," J. Aust. Math. Soc. 2 (1961) 153-188

[4] J. N. Lyness, "A Property of an Iteration
Process," J. Aust. Math. Soc. 2 (1961) 189-194

[5] Blatt, J. M., and J. N. Lyness, "The Practical Use of Variation
Principles in Non-Linear Mechanics," J. Aust. Math. Soc. 2
(1962) 357-368

[6] Blatt, J. M., G. H. Derrick, and J. N. Lyness, "Binding Energy of
the Triton," Phys. Rev. Letters 8 (1962) 323-325

[7] Delves, L. M., and J. N. Lyness, "Upper Bound on the Neutron
Deuteron Doublet scattering Length (I) Matrix Elements of the
Hamiltonian," Nucl. Phys. 45 (1963) 296-312

[8] Blatt, J. M., J. N. Lyness, and S. Y. Larsen, "The Three Body Bound
 State in He-4," Phys. Rev. 131 (1963) 2131-2132

[9] Mustard, D., J. N. Lyness, and J. M. Blatt, "Numerical Quadrature
in N Dimensions," Computer Journal 6 (1963) 75-87

[10] J. N. Lyness, and B. J. J. McHugh, "Integration over
Multidimensional Hypercubes (I) A Progressive Procedure," Computer
Journal 6 (1963) 264-270

[11] Delves, L. M., J. N. Lyness, and J. M. Blatt, "An Upper Bound on
the Neutron Deuteron 2-S Scattering Length," Phys. Rev. Letters 12
(1964) 542-544

[12] J. N. Lyness, "The Failure Rate in the University of Subtopia,"
Vestes 7 (1964) 260

[13] J. N. Lyness, "Symmetric Integration Rules for Hypercubes (I)
Error Coefficients," Math. Comp. 19 (1965) 260-276

[14] J. N. Lyness, "Symmetric Integration Rules for Hypercubes (II)
Rule Projection and Rule Extension," Math. Comp. 19 (1965) 394-407

[15] J. N. Lyness, "Integration Rules of Hypercubic Symmetry over a
Certain Spherically Symmetric Space," Math. Comp. 19 (1965) 471-476

[16] J. N. Lyness, "Limits on the Number of Function Evaluations
Required by Certain High Dimensional Integration Rules of Hypercubic
Symmetry," Math. Comp. 19 (1965) 625-637

[17] J. N. Lyness, "Symmetric Integration Rules for Hypercubes (III)
Construction of Integration Rules Using Null Rules," Math. Comp. 19
(1965) 638-643

[18] J. N. Lyness, "The Vector Triple Product Identity," Math. Gaz. L
(1966) 372

[19] J. N. Lyness, and C. B. Moler, "Van der Monde Systems and
Numerical Differentiation," Numer. Math. 8 (1966) 458-464

[20] J. N. Lyness, and B. W. Ninham, "Numerical Quadrature and
Asymptotic Expansions," Math. Comp. 21 (1967) 162-178

[21] J. N. Lyness, "The Calculation of Fourier Coefficients," SIAM
Journal of Num. Anal. 4 (1967) 301-315

[22] J. N. Lyness, and C. B. Moler, "Numerical Differentiation of
Analytic Functions," SIAM Journal of Num. Anal. 4 (1967) 202-210

[23] Delves, L. M., and J. N. Lyness, "A Numerical Method for Locating
the Zeros of an Analytic Function," Math. Comp. 21 (1967) 543-560

[24] J. N. Lyness, and L. M. Delves, "On Numerical Contour integration
Round a Closed Contour," Math. Comp. 21 (1967) 561-577

[25] J. N. Lyness, "A Trigonometric Inequality: Problem 67-6," SIAM
Review (1967) 250.

[26] J. N. Lyness, "Numerical Algorithms Based on the Theory of
Complex Variables," Proceedings of the ACM National Meeting 1967,
Thompson Book Co., Washington, D.C., 1967, 125-133

[27] J. N. Lyness, "Differentiation Formulas for Analytic Functions,"
Math. Comp. 22 (1968) 352-362

[28] J. N. Lyness, "The Calculation of Stieltjes' Integral,"
Numer. Math. 12 (1968) 252-265.

[29] B. W. Ninham and J.N.L., "Further Asymptotic Expansions for
the Error Functional," Math. Comp. 23 (1969) 71-84

[30] J. N. Lyness, and J. R. Gabriel, "Comment on a New Method for the
Evaluation of Multidimensional Integrals," J. Chem. Physics 50 (1969)
565-566

[31] Smith, W. E., and J. N. Lyness, "Applications of Hilbert
Transform Theory to Numerical Quadrature," Math. Comp. 23 (1969)
231-252

[32] J. N. Lyness, "Notes on the Adaptive Simpson Quadrature Routine,"
J. Assoc. Comp. Mach. 16 (1969) 483-495

[33] J. N. Lyness, "Quadrature Methods Based on Complex Function
Values," Math. Comp. 23 (1969) 601-620

[34] J. N. Lyness, "The Effect of Inadequate Convergence Criteria in
Automatic Routines," Comp. Journal 12 (1969) 279-281

[35] J. N. Lyness, and C. B. Moler, "Generalized Romberg Methods for
Integrals of Derivatives," Num. Math. 14 (1969) 1-13

[36] J. N. Lyness, "The Calculation of Fourier Coefficients by the
Mobius Inversion of the Poisson Summation Formula, Part I: Functions
whose early derivatives are contiuous," Math. Comp. 24 (1970) 101-135

[37] J. N. Lyness, "Algorithm 379 SQUANK (Simpson Quadrature Used
Adaptively - Noise Killed," Comm. ACM 13 (1970) 260-263

[38] J. N. Lyness, and B. J. J. McHugh, "On the Remainder Term in the
N-Dimensional Euler-Maclaurin Expansion," Numer. Math. 15 (1970)
333-344

[39] J. N. Lyness, "The Calculation of Fourier Coefficients by the
Mobius Inversion of the Poisson Summation Formula - Part II. Piecewise
Continuous Functions and Functions with Poles near the Interval
(0,1)," Math. Comp. 25 (1971) 59-78

[40] J. N. Lyness, "Adjusted Forms of the Fourier Coefficient
Asymptotic Expansion and Applications in Numerical Quadrature,"
Math. Comp. 25 (1971) 87-104

[41] J. N. Lyness, "The Calculation of Fourier Coefficients by the
Mobius Inversion of the Poisson Summation Formula - Part III.
Functions Having Algebraic Singularities," Math. Comp. 25 (1971)
483-493

[42] J. N. Lyness, and G. Sande, "Algorithm 413 ENTCAF and ENTCRE:
Evaluation of Normalized Taylor Coefficients of an Analytic Function,"
ACM 14 (1971) 669-675

[43] J. N. Lyness, "Guidelines for Automatic Quadrature Routines,"
Proceedings Information Processing Congress, Ljubljana, 1971,
North-Holland Publishing Co., Amsterdam, 1972, 1351-1355

[44] J. N. Lyness, "An Algorithm for Gauss-Romberg Integration," BIT
12 (1972) 194-203

[45] J. N. Lyness, and K. K. Puri, "The Euler Maclaurin Expansion for
the Simplex," Math. Comp. 27 (1973) 273-293

[46] J. N. Lyness, "Computational Techniques Based on the Lanczos
Representation," Math. Comp. 28 (1974) 81-123

[47] J. N. Lyness, and D. Jespersen, "Moderate Degree Symmetric
Quadrature Rules for the Triangle," J. Inst. of Math. & Applic. 15
(1975) 19-32

[48] C. S. Duris, and J. N. Lyness, "Compound Quadrature Rules for
the Product of Two Functions," SIAM J. Numer. Anal. 12 (1975) 681-697

[49] T. Strom, and J. N. Lyness "On Numerical Differentiation, BIT 15
(1975) 314-322

[50] J. N. Lyness, "An Error Functional Expansion for N-dimensional
Quadrature with an Integrand Function Singular at a Point,"
Math. Comp. 30 (1976) 1-23

[51] J. N. Lyness, and J. J. Kaganove, "Comments on the Nature of
Automatic Quadrature Routines," ACM Trans. on Math. Soft. 2 (1976)
65-81

[52] J. N. Lyness, "Applications of Extrapolation Techniques to
Multidimensional Quadrature of Some Integrand Functions with a
Singularity, " J. Comp. Physics 20 (1976) 346-364

[53] T. Howell, and J. N. Lyness, "On a Conjecture in
Multidimensional Quadrature," J. Comp. Phys. 21 (1976) 361-366
Academic Press, New York, 1977

[54] J. N. Lyness, and G. Monegato, "Quadrature Rules for Regions
Having Regular Hexagonal Symmetry," SIAM J. Numer. Anal. 14 (1977)
283-295

[55] J. N. Lyness, and J. J. Kaganove, "A Technique for Comparing
Automatic Quadrature Routines," The Computer J. 20 (1977) 170-177

[56] J. N. Lyness, "Quid, Quo, Quadrature?" The State of the Art in
Numerical Analysis, D. Jacobs, ed., Academic Press, New York, 1977,
pp. 535-560 (also Technical Memorandum ANL/MCS-TM-292)

[57] J. N. Lyness, "An Interface Problem in Numerical Software,"
 Proc. of the Sixth Manitoba Conference on Num. Math. and Computing,
 1976, 251-263

[58] J. N. Lyness, "Quadrature over a Simplex: Part 1. A
Representation for the Integrand Function," SIAM J. Numer. Anal. 15
(1978) 122-133

[59] J. N. Lyness, "Has Numerical Differentiation a Future?" Proc. of
the Seventh Manitoba Conference on Num. Math. and Computing," 1977,
107-129

[60] J. N. Lyness, "Quadrature over a Simplex: Part 2. A
Representation for the Error Functional," SIAM J. Numer. Anal. 15
(1978) 870-887

[61] J. N. Lyness, and P. Keast, "On p-Generator Fully Symmetric
Quadrature Rules," Numer. Math. 30 (1978) 51-63

[62] J. N. Lyness, "A Bench Mark Experiment for Minimization
Algorithms," Math. Comp. 33 (1979) 249-264

[63] J. N. Lyness, "The Affine Scale Invariance of Minimization
Algorithms," Math. Comp. 33 (1979) 265-287

[64] P. Keast, and J. N. Lyness, "On the Structure of Fully Symmetric
Multidimensional Quadrature Rules," SIAM J. Num. Anal. 16 (1979) 11-29

[65] G. Monegato, and J. N. Lyness, "On the Numerical Evaluation of a
Particular Singular Two-Dimensional Integral," Math. Comp. 33 (1979)
993-1002

[66] J. N. Lyness, "Performance Profiles and Software Evaluation,"
Performance Evaluation of Numerical Software, L. D. Fosdick, ed.,
North-Holland Publishing Co., 1979, 51-58

[67] J. N. Lyness, and A. C. Genz, "On Simplex Trapezoidal Rule
Families," SIAM J. Num. Anal. 17 (1980) 126-147

[68] J. N. Lyness, and G. Monegato, "Quadrature Error Functional
Expansion for the Simplex When the Integrand Function Has
Singularities at Vertices," Math. Comp. 34 (1980) 213-225

[69] F. N. Fritsch,  D. K. Kahaner, and J. N. Lyness, "Double
Integration Using One-Dimensional Adaptive Quadrature Routines: A
Software Interface Problem," ACM Trans. on Math. Soft. 7 (1981) 46-75

[70] J. N. Lyness, "Remarks about Performance Profiles," Problems and
Methodologies in Mathematical Software Production, Lecture Notes in
Computer Science, Vol. 142, P. C. Messina and A. Murli, eds.,
Springer-Verlag, Berlin, 1982, 186-97

[71] J. N. Lyness, and L. Gatteschi, "A Note on Cubature over a
Triangle of a Function Having Specified Singularities," International
Series of Numerical Math., Vol. 57, Numerical Integration,
Ed. G. Hammerlin, Birkhauser Verlag, Basel, 1982, 164-169

[72] J. N. Lyness, and L. Gatteschi, "On Quasi Degree Quadrature
Rules," Numer. Math. 39 (1982) 259-267

[73] B. Gabutti, and J. N. Lyness , "An Acceleration Method for the
Power Series of Entire Functions of Order 1," Math. Comp. 39 (1982)
587-597

[74] J. N. Lyness, "When not to use an Automatic Quadrature Routine,"
SIAM Rev. 25 (1983) 63-87

[75] L. Gatteschi, and J. N. Lyness, "An Indirect Approach to
Trigonometric Quadrature Rules," Calcolo Vol XX, fasc II 1983,
191-210

[76] J. N. Lyness, "The Calculation of Trigonometric Fourier
Coefficients," Jour. Comp. Phys. 54 (1984) 57-73

[77] J. N. Lyness, "Integrating some infinite oscillating Tails,"
Journal of Comp. and App. Math. 12&13 (1985) 109-117

[78] J. N. Lyness, "The Euler-Maclaurin Expansion for the Cauchy
Principal Value Integral," Num. Math. 46 (1985) 611-622

[79] B. Gabutti, and J. N. Lyness, "Some Generalisations of the
Euler-KnoTransformation," Numer. Math. 48 (1986) 199-220

[80] J. N. Lyness and G. Hines, "ALGORITHM 639; To Integrate Some
Infinite Oscillating Tails," ACM TOMS 12 (1986) 24-25

[81] J. N. Lyness, and G. Giunta, "A Modification of the Weeks' Method
for Numerical Inv. of the Laplace Transform," Math. Comp 47 (1986) 313-322

[82] J. N. Lyness, "Extrapolation Methods for Multi-Dimensional
Quadrature (of singular and regular Integrand Functions)," in
Numerical Algorithms, ed.  J.L.Mohamed and J.E.Walsh, Clar. Press,
Ox. Ap 1987, 105-124.  (See also ANL/MCS-TM-45)

[83] J. N. Lyness, and E. de Doncker-Kapenga, "On Quadrature Error
Expansions, Part I," Jour. Comp. App. Math. 17 (1987) 131-149

[84] J. N. Lyness, "Some Quadrature Rules for Finite Trigonometric and
 related Integrals" in Numerical Integration pp 17-33, eds. P Keast and
 G Fairweather Reidel Pub. Co. 1987.

[85] J. N. Lyness, and T. J. Kaper, "Calculating Fourier Transforms
of Long Tailed Functions," SIAM J. Sci. Stat. Comput. 8 (1987)
1005-1011

[86] B. S. Garbow, G. Giunta, J. N. Lyness, and A. Murli "Software for an
 Implementation of Weeks' Method for the Inverse Laplace Transform
 Problem," ACM Trans. Math. Softw. 14,2 (June 1988) 163-170

[87] B. S. Garbow, G. Giunta, J. N. Lyness, and A. Murli "Algorithm 662. A
 Fortran Software Package for the Numerical Inversion of the Laplace
 Transform Based on Weeks' Method." ACM Trans. Math. Softw. 14,2 (June
 1988) 171-176

[88] J. N. Lyness, "Some Comments on Quadrature Rule Construction
Criteria" International Series of Numerical Mathematics, Vol. 85,
Numerical Integration III, Ed. G. Hammerlin and H. Brass, Birkhauser
Verlag, Basel, 1988, 117-129

[89] I. H. Sloan and J. N. Lyness, "The Representation of Lattice
Quadrature Rules as Multiple Sums," Math. Comp 52 (1989) 81-94

[90] J. N. Lyness, and I. H. Sloan "Some Properties of Rank-2 Lattice
Rules," Math. Comp. 53 (1989) 627-637

[91] J. N. Lyness, "An Introduction to Lattice Rules and their
Generator Matrices," IMA Journal of Numerical Analysis 9 (1989)
405-419

[92] J. N. Lyness, and Newman, W., "A Search for Good Lattice Rules Based
on the Reciprocal Lattice Generator Matrix," Lecture Notes in
Comp. Sc.i 507, Springer-Verlag N.A. Sherwani, E.De D. and
J.A. Kap. (Eds.), 271-278

[93] J. N. Lyness and T. Sorevik, "The Number of Lattice Rules," BIT
29 (1989) 527-534

[94] I. H. Sloan and J. N. Lyness, "Lattice Rules: Projection Regularity
and Unique Representations," Math. Comp. 54 (1990) 649-660

[95] J. N. Lyness, T. Sorevik, and P. Keast, "Notes on Integration and
Integer Sublattices," Math. Comput. 56 (1991) 243-255

[96] J. N. Lyness, "Extrapolation-Based Boundary Element Quadrature,"
Rend. Sem. Mat. Univ. Pol. Torino, Fasc. Speciale 1991, Numerical
Methods, 189-203

[97] J. N. Lyness, and T. Sorevik, "A Search Program for Finding
Optimal Lattices," Computing 47 (1991) 103-120

[98] J. N. Lyness, "On Handling Singularities in Finite Elements," in
Numerical Integration, Ed. T.O.Espelid and A.Genz, Kluwer Academic
Publishers 1992, 219-233

[99] J. N. Lyness, and T. Sorevik, "An Algorithm for Finding Optimal
Integration Lattices of Composite Order," BIT 32 (1992) 665-675

[100] J. N. Lyness, "The Canonical Forms of a Lattice Rule," ISNM, Vol
112, Numerical Integration IV, Ed. G.Hammerlin +H.Brass, Birkhauser
Verlag, 1993, 225-240

[101] J. N. Lyness, and E. de Doncker-Kapenga, "On Quadrature Error
Expansions, Part II: The Full Corner Singularity," Numer. Math. 64
(1993) 355-370

[102] J. N. Lyness, and T. Sorevik, "Lattice Rules by Component
Scaling," Math. Comp. 61 (1993) 799-820

[103] J. N. Lyness and P. Keast, "Application of the Smith Normal Form to the
Structure of Lattice Rules," SIAM J. Matrix Anal. Al. 16 (1995) 218-231

[104] J. N. Lyness, and R. Cools, "A Survey of Numerical Cubature over
Triangles," Proc. Symp. Ap. Mat. 48 (1994) 127-150

[105] J. N. Lyness, "Quadrature over Curved Surfaces by Extrapolation,"
Math. Comp. 63 (1994) 727-740

[106] J. N. Lyness, "Finite-Part integrals and the Euler-Mac. Exp.,"  in
Approx. &Comput.  p. 397-407.  ISNM 119, Birkh\"auser Ver. 1994.
R.V.M. Zahar, ed.

[107] J. N. Lyness, and I. H. Sloan, "Cubature Rules of Prescribed Merit,"
SIAM J. Numer. Anal. 34 (1997) 586-602

[108] J. N. Lyness, and S. Joe, "Triangular Canonical Forms for Lattice
Rules of Prime-Power Order," Math. Comp. 65 (1996) 165-178 

[109] J. N. Lyness, "Evaluation of Minimization Software Based on
Performance Profile Techniques. pp152-4, THE QUALITY OF NUMERICAL
SOFTWARE Ed Ronald F. Boisvert Chapman & Hall 1997.

[110] J. N. Lyness, and U. Ruede, "Cubature of Integrands Containing
Derivatives,"  Numer. Math. 78 (1998) 439-461

[111] G. Monegato and J. N. Lyness, "The Euler-Maclaurin Expansion and
Finite- Part Integrals," Numer. Math. 81 (1999) 273-291

[112] P. Verlinden, D. M. Potts, and J. N. Lyness, "Error Expansions for
Multidimensional Trapezoidal Rules with Sidi Transformations," Numer. Alg.
16 (1997) 321-347

[113] J. N. Lyness, and L. M. Delves, "On the Implementation of a Modified
Sag-Szekeres Quadrature Method," JCAM 112, 189-200 (1999)

[114] J. N. Lyness and S. Joe, "A Constructive Approach to Lattice
Rule Canonical Forms," BIT 39 (1999) 701-715

[115] J. N. Lyness, "A Brief Survey of Extrapolation Quadrature," ANZIAM
J. 42 (2000) 181-184

[116] J. N. Lyness, and R. Cools, "Notes on a Search for Optimal
Lattice Rules: Cubature Formulae and their Applications: Ed M.V.Noskov
Krasnoyarsk STU. 2000; 259-273.  Available as Argonne National
Laboratory Preprint ANL/MCS-P829-0600, 2000.

[117]  J. N. Lyness, and R. Cools, "Notes on a Search for Optimal Lattice Rules:
Cubature Formulae and their Applications," ed. M. V. Noskov, Krasnoyarsk State
Technical University, 2000, pp. 259-273.  Available as Preprint ANL/MCS-P829-0600,
2000

[118]  R. Cools, and J. N. Lyness, "Three- and
Four-Dimensional K-Optimum Lattice Rules of Moderate Trigonometric
Degree," Math. Comp 70 (2001) 1549-1567 

[119]  J. N. Lyness, "Notes on Lattice Rules," J. of Complexity 19 (2003), pp. 321-331

[120]  J. N. Lyness and S. Joe, "The Number of Lattice Rules of Specified Upper
Class and Rank," BIT Numerical Mathematics 43 (2003), pp. 413-426

[121]  J. N. Lyness, and T. Sorevik, "Four Dimensional Lattice Rules Generated by
Skew-Circulant Matrices," Math. Comp. 73 (2003), pp. 279-295

[122]  J. N. Lyness, and G. Monegato, "Asymptotic Expansions for Two-Dimensional
Hypersingular Integrals," Numer. Math. 100 (2005) 293-329

[123] J. N. Lyness, "A Prototype Four-Dimensional Galerkin-Type Integral," Publ. RIMS,
Kyoto Univ. 41 (2005) 843-851

[124]  J. N. Lyness, "Extrapolation Expansions for Hanging-Chad-Type Galerkin
Integrals with Plane Triangular Elements," CPAA 5 (2006) 37-347

[125]  J. N. Lyness, and T. Sorevik, "Five-Dimensional K-Optimal Lattice Rules,"
Math. Comp. 75 (2006), pp, 1467-1480.  Also available as Argonne National
Laboratory Preprint ANL/MCS-P1244-0105, 2005.

[126]  J. N. Lyness, and S. Joe, "Determination of the Rank of an Integration
Lattice," BIT Numerical Mathematics 48 (2008), pp. 79-93.  Also available
as Argonne National Laboratory Preprint ANL/MCS-P1404-0307, 2007.

[127]  J. N. Lyness, "Numerical Evaluation of a Fixed-Amplitude Variable-Phase
Integral," Numer. Algor. 49 (2008), pp. 235-249

TECHNICAL MEMORANDA

This list excludes preprints of subsequently published papers.

J. N. Lyness, "Quid, Quo, Quadrature?" Technical Memorandum ANL/MCS-TM-292

J. N. Lyness and C. Greenwell, "A Pilot Scheme for Minimization
Soft. Eval.," Technical Memorandum ANL/MCS-TM-323 (1978)

J. N. Lyness, "Performance Profiles and Software Evaluation," Technical Memorandum ANL/MCS-TM-343
(1979)

J. N. Lyness, "Remarks about Performance Profiles," Technical Memorandum ANL/MCS-TM-369 (1981)

J. N. Lyness, "QUG1: Trigonometric Fourier Coefficients," Technical Memorandum ANL/MCS-TM-370
(1981)

J. N. Lyness, "QUG2: Integration over a Triangle," Technical Memorandum ANL/MCS-TM-13
(August 1983)

J. N. Lyness and G.Giunta, "A Modification of the Weeks' Method for
Numerical Inversion of the Laplace Transform," Technical Memorandum ANL/MCS-TM-35 (October
1984)

G.Giunta, J. N. Lyness, and A.Murli "An Implementation of Weeks'
Method for the Inverse Laplace Transform Problem," Technical Memorandum ANL/MCS-TM-39
(October 1984)

J. N. Lyness,"Extrapolation Methods for Multi-dimensional Quadrature
of Singular and Regular Integrand Functions," Technical Memorandum ANL/MCS-TM-45 (February
1985)

J. N. Lyness and W. Newman, "A Classification of Lattice Rules using
the Reciprocal Lattice Generator Matrix," Report ANL-89/20

J. N. Lyness and S. Plowman, "Trapezoidal Rule Quadrature Algorithms for
MIMD Distributed Memory Computers," Preprint ANL/MCS-P342-1292