References
Abramowitz and Stegun
Abramowitz, Milton, and Irene A. Stegun (editors) (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington.
Ahrens and Dieter
Ahrens, J.H., and U. Dieter (1974), Computer methods for sampling from gamma, beta, Poisson, and binomial distributions, Computing, 12, 223–246.
Akima
Akima, H. (1970), A new method of interpolation and smooth curve fitting based on local procedures, Journal of the ACM, 17, 589–602.
Akima, H. (1978), A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points, ACM Transactions on Mathematical Software, 4, 148–159.
Altman and Gondzio
Altman, Anna, and Jacek Gondzio (1998), Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization, Logilab Technical Report 1998.6, Logilab, HEC Geneva, Section of Management Studies, Geneva.
Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen (1999), LAPACK Users' Guide, 3rd ed., SIAM, Philadelphia.
Ashcraft
Ashcraft, C. (1987), A vector implementation of the multifrontal method for large sparse symmetric positive definite systems, Technical Report ETA-TR-51, Engineering Technology Applications Division, Boeing Computer Services, Seattle, Washington.
Ashcraft et al.
Ashcraft, C., R. Grimes, J. Lewis, B. Peyton, and H. Simon (1987), Progress in sparse matrix methods for large linear systems on vector supercomputers. Intern. J. Supercomputer Applic., 1(4), 10–29.
Atkinson (1979)
Atkinson, A.C. (1979), A family of switching algorithms for the computer generation of beta random variates, Biometrika, 66, 141–145.
Atkinson (1978)
Atkinson, Ken (1978), An Introduction to Numerical Analysis, John Wiley & Sons, New York.
Barnett
Barnett, A.R. (1981), An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy, Computer Physics Communication, 21, 297–314.
Barrett and Healy
Barrett, J.C., and M. J.R. Healy (1978), A remark on Algorithm AS 6: Triangular decomposition of a symmetric matrix, Applied Statistics, 27, 379–380.
Bays and Durham
Bays, Carter, and S.D. Durham (1976), Improving a poor random number generator, ACM Transactions on Mathematical Software, 2, 59–64.
Beckers
Beckers, Stan (1980), The Constant Elasticity of Variance Model and Its Implications For Option Pricing , The Journal of Finance, Vol. 35, No. 3, pp. 661-673.
Bini
Bini, D. A. (1996), Numerical computation of polynomial zeros by means of Aberth's method, Numerical Algorithms 13,179-200.
Blom
Blom, Gunnar (1958), Statistical Estimates and Transformed Beta-Variables, John Wiley & Sons, New York.
Blom and Zegeling
Blom, JG, and Zegeling, PA (1994), A Moving-grid Interface for Systems of One-dimensional Time-dependent Partial Differential Equations, ACM Transactions on Mathematical Software, Vol 20, No.2, 194-214.
Boisvert
Boisvert, Ronald (1984), A fourth order accurate fast direct method of the Helmholtz equation, Elliptic Problem solvers II, (edited by G. Birkhoff and A. Schoenstadt), Academic Press, Orlando, Florida, 35–44.
Bosten and Battiste
Bosten, Nancy E., and E.L. Battiste (1974), Incomplete beta ratio, Communications of the ACM, 17, 156–157.
Brenan, Campbell, and Petzold
Brenan, K.E., S.L. Campbell, L.R. Petzold (1989), Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Elseview Science Publ. Co.
Brent
Brent, Richard P. (1973), Algorithms for Minimization without Derivatives, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
Brent, R.P. (1971), An Algorithm With Guaranteed Convergence for Finding a Zero of a Function, The Computer Journal, 14, 422−425.
Brigham
Brigham, E. Oran (1974), The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, New Jersey.
Burgoyne
Burgoyne, F.D. (1963), Approximations to Kelvin functions, Mathematics of Computation, 83, 295-298.
Carlson
Carlson, B.C. (1979), Computing elliptic integrals by duplication, Numerische Mathematik, 33, 1−16.
Carlson and Notis
Carlson, B.C., and E.M. Notis (1981), Algorithms for incomplete elliptic integrals, ACM Transactions on Mathematical Software, 7, 398–403.
Carlson and Foley
Carlson, R.E., and T.A. Foley (1991),The parameter R2 in multiquadric interpolation, Computer Mathematical Applications, 21, 29–42.
Cheng
Cheng, R.C.H. (1978), Generating beta variates with nonintegral shape parameters, Communications of the ACM, 21, 317–322.
Cohen and Taylor
Cohen, E. Richard, and Barry N. Taylor (1986), The 1986 Adjustment of the Fundamental Physical Constants, Codata Bulletin, Pergamon Press, New York.
Cooley and Tukey
Cooley, J.W., and J.W. Tukey (1965), An algorithm for the machine computation of complex Fourier series, Mathematics of Computation, 19, 297–301.
Cooper
Cooper, B.E. (1968), Algorithm AS4, An auxiliary function for distribution integrals, Applied Statistics, 17, 190–192.
Courant and Hilbert
Courant, R., and D. Hilbert (1962), Methods of Mathematical Physics, Volume II, John Wiley & Sons, New York, NY.
Craven and Wahba
Craven, Peter, and Grace Wahba (1979), Smoothing noisy data with spline functions, Numerische Mathematik, 31, 377–403.
Crowe et al.
Crowe, Keith, Yuan-An Fan, Jing Li, Dale Neaderhouser, and Phil Smith (1990), A direct sparse linear equation solver using linked list storage, IMSL Technical Report 9006, IMSL, Houston.
Davis and Rabinowitz
Davis, Philip F., and Philip Rabinowitz (1984), Methods of Numerical Integration, Academic Press, Orlando, Florida.
de Boor
de Boor, Carl (1978), A Practical Guide to Splines, Springer-Verlag, New York.
Demmel et al.
Demmel, J.W., J.R. Gilbert, and X.S. Li, (1999), SuperLU Users’ Guide, Tech. Rep. LBNL‑44289, Lawrence Berkeley National Laboratory.
Demmel, J.W., S.C. Eisenstat, J.R. Gilbert, X.S. Li, and J.W.H. Liu, (1999), A Supernodal Approach To Sparse Partial Pivoting, SIAM Journal on Matrix Analysis and its Applications, 20, 720-755.
Demmel, J.W., J. R. Gilbert, and X. S. Li (1999c) , An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination, SIAM Journal on Matrix Analysis and its Applications, 20(4), 915- 952.
Dennis and Schnabel
Dennis, J.E., Jr., and Robert B. Schnabel (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey.
Dongarra et al.
Dongarra, J.J., J.R. Bunch, C.B. Moler, and G.W. Stewart (1979), LINPACK User’s Guide, SIAM, Philadelphia.
Doornik
Doornik, J. A., An Improved Ziggurat Method to Generate Normal Random Samples, http://www.doornik.com/research/ziggurat.pdf.
Draper and Smith
Draper, N.R., and H. Smith (1981), Applied Regression Analysis, 2nd. ed., John Wiley & Sons, New York.
DuCroz et al.
Du Croz, Jeremy, P. Mayes, and G. Radicati (1990), Factorization of band matrices using Level-3 BLAS, Proceedings of CONPAR 90-VAPP IV, Lecture Notes in Computer Science, Springer, Berlin, 222.
Duff et al.
Duff, I. S., A. M. Erisman, and J. K. Reid (1986), Direct Methods for Sparse Matrices, Clarendon Press, Oxford.
Duff et al.
Duff, Ian S., R. G. Grimes, and J. G. Lewis (1992) first ed, Users’ Guide for the Harwell-Boeing Sparse Matrix Collection, CERFACS, Toulouse Cedex, France.
Duff and Reid
Duff, I.S., and J.K. Reid (1983), The multifrontal solution of indefinite sparse symmetric linear equations. ACM Transactions on Mathematical Software, 9, 302–325.
Duff, I.S., and J.K. Reid (1984), The multifrontal solution of unsymmetric sets of linear equations. SIAM Journal on Scientific and Statistical Computing, 5, 633–641.
Enright and Pryce
Enright, W.H., and J.D. Pryce (1987), Two FORTRAN packages for assessing initial value methods, ACM Transactions on Mathematical Software, 13, 1–22.
Farebrother and Berry
Farebrother, R.W., and G. Berry (1974), A remark on Algorithm AS 6: Triangular decomposition of a symmetric matrix, Applied Statistics, 23, 477.
Fernando and Parlett
Fernando, K. V., and B. N. Parlett (1994), Accurate singular values and differential qd algorithms, Numerische Mathematik, 67, 191-229.
Fisher
Fisher, R.A. (1936), The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7, 179– 188.
Fishman and Moore
Fishman, George S. and Louis R. Moore (1982), A statistical evaluation of multiplicative congruential random number generators with modulus 231 – 1, Journal of the American Statistical Association, 77, 129–136.
Forsythe
Forsythe, G.E. (1957), Generation and use of orthogonal polynomials for fitting data with a digital computer, SIAM Journal on Applied Mathematics, 5, 74–88.
Franke
Franke, R. (1982), Scattered data interpolation: Tests of some methods, Mathematics of Computation, 38, 181–200.
Garbow et al.
Garbow, B.S., J.M. Boyle, K.J. Dongarra, and C.B. Moler (1977), Matrix Eigensystem Routines - EISPACK Guide Extension, Springer–Verlag, New York.
Garbow, B.S., G. Giunta, J.N. Lyness, and A. Murli (1988), Software for an implementation of Weeks’ method for the inverse Laplace transform problem, ACM Transactions on Mathematical Software, 14, 163–170.
Gautschi
Gautschi, Walter (1968), Construction of Gauss-Christoffel quadrature formulas, Mathematics of Computation, 22, 251–270.
Gautschi, Walter (1969), Complex error function, Communications of the ACM, 12, 635. Gautschi, Walter (1970), Efficient computation of the complex error function, SIAM Journal on Mathematical Analysis, 7, 187198.
Gear
Gear, C.W. (1971), Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey.
Gentleman
Gentleman, W. Morven (1974), Basic procedures for large, sparse or weighted linear least squares problems, Applied Statistics, 23, 448–454.
George and Liu
George, A., and J.W.H. Liu (1981), Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, New Jersey.
Gill and Murray
Gill, Philip E., and Walter Murray (1976), Minimization subject to bounds on the variables, NPL Report NAC 92, National Physical Laboratory, England.
Gill et al.
Gill, P.E., W. Murray, M.A. Saunders, and M.H. Wright (1985), Model building and practical aspects of nonlinear programming, in Computational Mathematical Programming, (edited by K. Schittkowski), NATO ASI Series, 15, Springer-Verlag, Berlin, Germany.
Gill, P.E., W. Murray, and M.H. Wright (1981), Practical Optimization, Academic Press Inc. Limited, London.
Goldfarb and Idnani
Goldfarb, D., and A. Idnani (1983), A numerically stable dual method for solving strictly convex quadratic programs, Mathematical Programming, 27, 1–33.
Golub
Golub, G.H. (1973), Some modified matrix eigenvalue problems, SIAM Review, 15, 318–334.
Golub and Van Loan
Golub, G.H., and C.F. Van Loan (1989), Matrix Computations, Second Edition, The Johns Hopkins University Press, Baltimore, Maryland.
Golub, Gene H., and Charles F. Van Loan (1983), Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland.
Golub and Welsch
Golub, G.H., and J.H. Welsch (1969), Calculation of Gaussian quadrature rules, Mathematics of Computation, 23, 221–230.
Gondzio (1994)
Gondzio, Jacek (1994), Multiple Centrality Corrections in a Primal-Dual Method for Linear Programming, Logilab Technical Report 1994.20, Logilab, HEC Geneva, Section of Management Studies, Geneva.
Gondzio (1995)
Gondzio, Jacek (1995), HOPDM - Modular Solver for LP Problems, User's Guide to version 2.12, WP-95-50, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Gregory and Karney
Gregory, Robert, and David Karney (1969), A Collection of Matrices for Testing Computational Algorithms, Wiley-Interscience, John Wiley & Sons, New York.
Griffin and Redfish
Griffin, R., and K A. Redish (1970), Remark on Algorithm 347: An efficient algorithm for sorting with minimal storage, Communications of the ACM, 13, 54.
Grosse
Grosse, Eric (1980), Tensor spline approximation, Linear Algebra and its Applications, 34, 29–41.
Guerra and Tapia
Guerra, V., and R. A. Tapia (1974), A local procedure for error detection and data smoothing, MRC Technical Summary Report 1452, Mathematics Research Center, University of Wisconsin, Madison.
Hageman and Young
Hageman, Louis A., and David M. Young (1981), Applied Iterative Methods, Academic Press, New York.
Hanson
Hanson, Richard J. (1986), Least squares with bounds and linear constraints, SIAM Journal Sci. Stat. Computing, 7, #3.
Hanson
Hanson, R. J. (2008), Integrating Feynman-Kac Equations Using Hermite Quintic Finite Elements, White Paper.
Hanson and Krogh
Hanson, R. J., and Krogh, F. T., (2008), Solving Constrained Differential-Algebraic Systems Using Projections, White Paper.
Hardy
Hardy, R.L. (1971), Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research, 76, 1905–1915.
Hart et al.
Hart, John F., E.W. Cheney, Charles L. Lawson, Hans J.Maehly, Charles K. Mesztenyi, John R. Rice, Henry G. Thacher, Jr., and Christoph Witzgall (1968), Computer Approximations, John Wiley & Sons, New York.
Healy
Healy, M.J.R. (1968), Algorithm AS 6: Triangular decomposition of a symmetric matrix, Applied Statistics, 17, 195–197.
Herraman
Herraman, C. (1968), Sums of squares and products matrix, Applied Statistics, 17, 289–292.
Higham
Higham, Nicholas J. (1988), FORTRAN Codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation, ACM Transactions on Mathematical Software, 14, 381-396.
Hill
Hill, G.W. (1970), Student’s t-distribution, Communications of the ACM, 13, 617–619.
Hindmarsh
Hindmarsh, A.C. (1974), GEAR: Ordinary Differential Equation System Solver, Lawrence Livermore National Laboratory Report UCID-30001, Revision 3, Lawrence Livermore National Laboratory, Livermore, Calif.
Hinkley
Hinkley, David (1977), On quick choice of power transformation, Applied Statistics, 26, 67–69.
Huber
Huber, Peter J. (1981), Robust Statistics, John Wiley & Sons, New York.
Hull et al.
Hull, T.E., W.H. Enright, and K.R. Jackson (1976), User’s guide for DVERK — A subroutine for solving nonstiff ODEs, Department of Computer Science Technical Report 100, University of Toronto.
Irvine et al.
Irvine, Larry D., Samuel P. Marin, and Philip W. Smith (1986), Constrained interpolation and smoothing, Constructive Approximation, 2, 129–151.
Jackson et al.
Jackson, K.R., W.H. Enright, and T.E. Hull (1978), A theoretical criterion for comparing Runge-Kutta formulas, SIAM Journal of Numerical Analysis, 15, 618–641.
Jenkins
Jenkins, M.A. (1975), Algorithm 493: Zeros of a real polynomial, ACM Transactions on Mathematical Software, 1, 178–189.
Jenkins and Traub
Jenkins, M.A., and J.F. Traub (1970), A three-stage algorithm for real polynomials using quadratic iteration, SIAM Journal on Numerical Analysis, 7, 545–566.
Jenkins, M.A., and J.F. Traub (1970), A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numerishe Mathematik, 14, 252–263.
Jenkins, M.A., and J.F. Traub (1972), Zeros of a complex polynomial, Communications of the ACM, 15, 97– 99.
Jöhnk
Jöhnk, M.D. (1964), Erzeugung von Betaverteilten und Gammaverteilten Zufalls-zahlen, Metrika, 8, 5–15.
Kendall and Stuart
Kendall, Maurice G., and Alan Stuart (1973), The Advanced Theory of Statistics, Volume II, Inference and Relationship, Third Edition, Charles Griffin & Company, London, Chapter 30.
Kennedy and Gentle
Kennedy, William J., Jr., and James E. Gentle (1980), Statistical Computing, Marcel Dekker, New York.
Kernighan and Richtie
Kernighan, Brian W., and Richtie, Dennis M. 1988, "The C Programming Language" Second Edition, 241.
Kinnucan and Kuki
Kinnucan, P., and Kuki, H., (1968), A single precision inverse error function subroutine, Computation Center, University of Chicago.
Knuth
Knuth, Donald E. (1981), The Art of Computer Programming, Volume II: Seminumerical Algorithms, 2nd. ed., Addison-Wesley, Reading, Mass.
Kochanek and Bartels
Kochanek, Doris H. U., and Bartels, Richard H (1984), Interpolating Splines with Local Tension, Continuity, and Bias Control, ACM SIGGRAPH, vol. 18, no. 3, pp. 33–41.
Krogh, Fred, T. (2005), An Algorithm for Linear Programming, http://mathalacarte.com/fkrogh/pub/lp.pdf, Tujunga, CA.
Krogh, Fred, T. (1974), "Changing Stepsize in the Integration of Differential Equations Using Modified Divided Differences" in Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations,Springer Verlag, Berlin, no. 362, pp. 22-71.
Krogh, Fred T. (1970), Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation, Math. of Comp. 24, 109, 185-190.
Learmonth and Lewis
Learmonth, G.P., and P.A.W. Lewis (1973), Naval Postgraduate School Random Number Generator Package LLRANDOM, NPS55LW73061A, Naval Postgraduate School, Monterey, California.
Lehmann
Lehmann, E.L. (1975), Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, San Francisco.
Lehoucq, R.B., Sorensen, D.C., and Yang, C. (1998), ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Society for Industrial and Applied Mathematics, Philadelphia PA.
Levenberg
Levenberg, K. (1944), A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics, 2, 164–168.
Leavenworth
Leavenworth, B. (1960), Algorithm 25: Real zeros of an arbitrary function, Communications of the ACM, 3, 602.
Lentini and Pereyra
Pereyra, Victor (1978), PASVA3: An adaptive finite-difference FORTRAN program for first order nonlinear boundary value problems, in Lecture Notes in Computer Science, 76, Springer-Verlag, Berlin, 67−88.
Lewis et al.
Lewis, P.A.W., A.S. Goodman, and J.M. Miller (1969), A pseudorandom number generator for the System/ 360, IBM Systems Journal, 8, 136–146.
Liepman
Liepman, David S. (1964), Mathematical constants, in Handbook of Mathematical Functions, Dover Publications, New York.
Liu
Liu, J.W.H. (1987), A collection of routines for an implementation of the multifrontal method, Technical Report CS-87-10, Department of Computer Science, York University, North York, Ontario, Canada.
Liu, J.W.H. (1989), The multifrontal method and paging in sparse Cholesky factorization. ACM Transactions on Mathematical Software, 15, 310-325.
Liu, J.W.H. (1990), The multifrontal method for sparse matrix solution: theory and practice, Technical Report CS-90-04, Department of Computer Science, York University, North York, Ontario, Canada.
Liu, J.W.H. (1986), On the storage requirement in the out-of-core multifrontal method for sparse factorization. ACM Transactions on Mathematical Software, 12, 249-264.
Lyness and Giunta
Lyness, J.N. and G. Giunta (1986), A modification of the Weeks Method for numerical inversion of the Laplace transform, Mathematics of Computation, 47, 313–322.
Madsen and Sincovec
Madsen, N.K., and R.F. Sincovec (1979), Algorithm 540: PDECOL, General collocation software for partial differential equations, ACM Transactions on Mathematical Software, 5, #3, 326–351.
Maindonald
Maindonald, J.H. (1984), Statistical Computation, John Wiley & Sons, New York.
Marquardt
Marquardt, D. (1963), An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics, 11, 431–441.
Marsaglia and Tsang
Marsaglia, G. and Tsang, W. W (2000), The Ziggurat Method for Generating Random Variables, Journal of Statistical Software, Volume 5-8, pages 1-7.
Martin and Wilkinson
Martin, R.S., and J.H. Wilkinson (1971), Reduction of the Symmetric Eigenproblem Ax = λBx and Related Problems to Standard Form, Volume II, Linear Algebra Handbook, Springer, New York.
Martin, R.S., and J.H. Wilkinson (1971), The Modified LR Algorithm for Complex Hessenberg Matrices, Handbook, Volume II, Linear Algebra, Springer, New York.
Mayle
Mayle, Jan, (1993), Fixed Income Securities Formulas for Price, Yield, and Accrued Interest, SIA Standard Securities Calculation Methods, Volume I, Third Edition, pages 17-35.
Michelli
Micchelli, C.A. (1986), Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constructive Approximation, 2, 11–22.
Michelli et al.
Micchelli, C.A., T.J. Rivlin, and S. Winograd (1976), The optimal recovery of smooth functions, Numerische Mathematik, 26, 279–285.
Micchelli, C.A., Philip W. Smith, John Swetits, and Joseph D. Ward (1985), Constrained Lp approximation, Constructive Approximation, 1, 93–102.
Moler and Stewart
Moler, C., and G.W. Stewart (1973), An algorithm for generalized matrix eigenvalue problems, SIAM Journal on Numerical Analysis, 10, 241-256.
Moré et al.
Moré, Jorge, Burton Garbow, and Kenneth Hillstrom (1980), User Guide for MINPACK-1, Argonne National Laboratory Report ANL-80-74, Argonne, Illinois.
Müller
Müller, D.E. (1956), A method for solving algebraic equations using an automatic computer, Mathematical Tables and Aids to Computation, 10, 208–215.
Murtagh
Murtagh, Bruce A. (1981), Advanced Linear Programming: Computation and Practice, McGraw-Hill, New York.
Murty
Murty, Katta G. (1983), Linear Programming, John Wiley and Sons, New York.
Nelder and Mead
Nelder, J.A., and Mead, R. (1965), A simplex method for function minimization, The Computer Journal, 7(4), 308-313.
Neter and Wasserman
Neter, John, and William Wasserman (1974), Applied Linear Statistical Models, Richard D. Irwin, Homewood, Illinois.
Neter et al.
Neter, John, William Wasserman, and Michael H. Kutner (1983), Applied Linear Regression Models, Richard D. Irwin, Homewood, Illinois.
Ogita et al.
Ogita, T., S. M. Rump, and S. Oishi (2005), Accurate Sum and Dot Product, SIAM J. Sci. Comput., 26(6), 1955-1988.
Østerby and Zlatev
Østerby, Ole, and Zahari Zlatev (1982), Direct Methods for Sparse Matrices, Lecture Notes in Computer Science, 157, Springer-Verlag, New York.
Owen
Owen, D.B. (1962), Handbook of Statistical Tables, Addison-Wesley Publishing Company, Reading, Mass.
Owen, D.B. (1965), A special case of the bivariate non-central t distribution, Biometrika, 52, 437−446.
Parlett
Parlett, B.N. (1980), The Symmetric Eigenvalue Problem, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
Patefield, W.M. and Tandy, D. (2000), Fast and Accurate Calculation of Owen’s T‑Function, J. Statistical Software, 5, Issue 5, 1-25.
Pennington and Berzins
Pennington, S. V., Berzins, M., (1994), Software for first-order partial differential equations. 63−99.
Petro
Petro, R. (1970), Remark on Algorithm 347: An efficient algorithm for sorting with minimal storage, Communications of the ACM, 13, 624.
Petzold
Petzold, L.R. (1982), A description of DASSL: A differential/ algebraic system solver, Proceedings of the IMACS World Congress, Montreal, Canada.
Piessens et al.
Piessens, R., E. deDoncker-Kapenga, C.W. Überhuber, and D.K. Kahaner (1983), QUADPACK, Springer-Verlag, New York.
Powell
Powell, M.J.D. (1978), A fast algorithm for nonlinearly constrained optimization calculations, Numerical Analysis Proceedings, Dundee 1977, Lecture Notes in Mathematics, (edited by G. A. Watson), 630, Springer-Verlag, Berlin, Germany, 144–157.
Powell, M.J.D. (1985), On the quadratic programming algorithm of Goldfarb and Idnani, Mathematical Programming Study, 25, 46–61.
Powell, M.J.D. (1988), A tolerant algorithm for linearly constrained optimizations calculations, DAMTP Report NA17, University of Cambridge, England.
Powell, M.J.D. (1989), TOLMIN: A fortran package for linearly constrained optimizations calculations, DAMTP Report NA2, University of Cambridge, England.
Powell, M.J.D. (1983), ZQPCVX a FORTRAN subroutine for convex quadratic programming, DAMTP Report 1983/NA17, University of Cambridge, Cambridge, England.
Powell, M.J.D. (2004), Least Frobenius norm updating of quadratic models that satisfy interpolation conditions, Mathematical Programming, 100(1), 183-215.
Powell, M.J.D. (2014), On fast trust region methods for quadratic models with linear constraints, DAMTP report 2014/NA02, University of Cambridge, Cambridge, England.
Ralston, Anthony (1965), A First Course in Numerical Analysis, McGraw-Hill, NY.
Rauber et. al.
Rauber, T., G. Rünger, and C. Scholtes (1999), Scalability of Sparse Cholesky Factorization, International Journal of High Speed Computing, 10, No. 1, 19 - 52.
Reinsch
Reinsch, Christian H. (1967), Smoothing by spline functions, Numerische Mathematik, 10, 177−183.
Rice
Rice, J.R. (1983), Numerical Methods, Software, and Analysis, McGraw-Hill, New York.
Saad and Schultz
Saad, Y., and M. H. Schultz (1986), GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems, SIAM Journal of Scientific and Statistical Computing, 7, 856-869.
Salane, D.E. (1986), Adaptive Routines for Forming Jacobians Numerically, SAND86-1319, Sandia National Laboratories.
Sallas and Lionti
Sallas, William M., and Abby M. Lionti (1988), Some useful computing formulas for the nonfull rank linear model with linear equality restrictions, IMSL Technical Report 8805, IMSL, Houston.
Savage
Savage, I. Richard (1956), Contributions to the theory of rank order statistics—the two-sample case, Annals of Mathematical Statistics, 27, 590–615.
Schmeiser
Schmeiser, Bruce (1983), Recent advances in generating observations from discrete random variates, in Computer Science and Statistics: Proceedings of the Fifteenth Symposium on the Interface, (edited by James E. Gentle), North-Holland Publishing Company, Amsterdam, 154–160.
Schmeiser and Babu
Schmeiser, Bruce W., and A.J.G. Babu (1980), Beta variate generation via exponential majorizing functions, Operations Research, 28, 917–926.
Schmeiser and Kachitvichyanukul
Schmeiser, Bruce, and Voratas Kachitvichyanukul (1981), Poisson Random Variate Generation, Research Memorandum 81–4, School of Industrial Engineering, Purdue University, West Lafayette, Indiana.
Schmeiser and Lal
Schmeiser, Bruce W., and Ram Lal (1980), Squeeze methods for generating gamma variates, Journal of the American Statistical Association, 75, 679–682.
Seidler and Carmichael
Seidler, Lee J. and Carmichael, D.R., (editors) (1980), Accountants' Handbook, Volume I, Sixth Edition, The Ronald Press Company, New York.
Sewell, Granville (2005), Computational Methods of Linear Algebra, second edition, John Wiley & Sons, New York.
Shampine
Shampine, L.F. (1975), Discrete least squares polynomial fits, Communications of the ACM, 18, 179–180.
Shampine and Gear
Shampine, L.F. and C.W. Gear (1979), A user’s view of solving stiff ordinary differential equations, SIAM Review, 21, 1–17.
Sincovec and Madsen
Sincovec, R.F., and N.K. Madsen (1975), Software for nonlinear partial differential equations, ACM Transactions on Mathematical Software, 1, #3, 232–260.
Singleton
Singleton, T.C. (1969), Algorithm 347: An efficient algorithm for sorting with minimal storage, Communications of the ACM, 12, 185–187.
Smith et al.
Smith, B.T., J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V.C. Klema, and C.B. Moler (1976), Matrix Eigensystem Routines — EISPACK Guide, Springer-Verlag, New York.
Smith
Smith, P.W. (1990), On knots and nodes for spline interpolation, Algorithms for Approximation II, J.C. Mason and M.G. Cox, Eds., Chapman and Hall, New York.
Sorensen, D.C. (1992), Implicit Application of Polynomial Filters in a k-Step Arnoldi Method, SIAM Journal on Matrix Analysis and Applications, 13(1): 357-385.
Spellucci, Peter
Spellucci, P. (1998), An SQP method for general nonlinear programs using only equality constrained subproblems, Math. Prog., 82, 413-448, Physica Verlag, Heidelberg, Germany
Spellucci, P. (1998), A new technique for inconsistent problems in the SQP method. Math. Meth. of Oper. Res.,47, 355-500, Physica Verlag, Heidelberg, Germany.
Stewart
Stewart, G.W. (1973), Introduction to Matrix Computations, Academic Press, New York.
Strecok
Strecok, Anthony J. (1968), On the calculation of the inverse of the error function, Mathematics of Computation, 22, 144–158.
Stroud and Secrest
Stroud, A.H., and D.H. Secrest (1963), Gaussian Quadrature Formulae, Prentice-Hall, Englewood Cliffs, New Jersey.
Temme
Temme, N.M (1975), On the numerical evaluation of the modified Bessel Function of the third kind, Journal of Computational Physics, 19, 324–337.
Tezuka
Tezuka, S. (1995), Uniform Random Numbers: Theory and Practice. Academic Publishers, Boston.
Thompson and Barnett
Thompson, I.J. and A.R. Barnett (1987), Modified Bessel functions Iν(z) and Kν(z) of real order and complex argument, Computer Physics Communication, 47, 245–257.
Tukey
Tukey, John W. (1962), The future of data analysis, Annals of Mathematical Statistics, 33, 1–67.
Velleman and Hoaglin
Velleman, Paul F., and David C. Hoaglin (1981), Applications, Basics, and Computing of Exploratory Data Analysis, Duxbury Press, Boston
Verwer et al
Verwer, J. G., Blom, J. G., Furzeland, R. M., and Zegeling, P. A. (1989), A moving-grid method for one-dimensional PDEs Based on the Method of Lines, Adaptive Methods for Partial Differential Equations, Eds., J. E. Flaherty, P. J. Paslow, M. S. Shephard, and J. D. Vasiilakis, SIAM Publications, Philadelphia, PA (USA) pp. 160-175.
Walker
Walker, H.F. (1988), Implementation of the GMRES method using Householder transformations, SIAM Journal of Scientific and Statistical Computing, 9, 152-163.
Watkins
Watkins, David S., L. Elsner (1991), Convergence of algorithm of decomposition type for the eigenvalue problem, Linear Algebra Applications, 143, pp. 29–47.
Weeks
Weeks, W.T. (1966), Numerical inversion of Laplace transforms using Laguerre functions, J. ACM, 13, 419–429.
Wilmott et al
Wilmott, P., Howison, and S., Dewynne, J., (1996), The Mathematics of Financial Derivatives (A Student Introduction), Cambridge Univ. Press, New York, NY. 317 pages.
