Appendix B References
Adams
Adams et al. (2008), The Fortran 2003 Handbook: The Complete Syntax, Features and Procedures, 561.
Aird and Howell
Aird, Thomas J., and Byron W. Howell (1991), IMSL Technical Report 9103, IMSL, Houston.
Aird and Rice
Aird, T.J., and J.R. Rice (1977), Systematic search in high dimensional sets, SIAM Journal on Numerical Analysis, 14, 296‑312.
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, 148159.
Anderson et al.
Anderson, E., Bai, Z., Bishop, C., Blackford, S., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D. (1999), LAPACK Users’ Guide, SIAM, 3rd ed., Philadelphia.
Arushanian et al.
Arushanian, O.B., M.K. Samarin, V.V. Voevodin, E.E. Tyrtyshikov, B.S. Garbow, J.M. Boyle, W.R. Cowell, and K.W. Dritz (1983), The TOEPLITZ Package Users’ Guide, Argonne National Laboratory, Argonne, Illinois.
Ashcraft
Ashcraft, C. (1987), A vector implementation of the multifrontal method for large sparse, symmetric positive definite linear 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
Atkinson, Ken (1978), An Introduction to Numerical Analysis, John Wiley & Sons, New York.
Atchison
Atchison, M.A., and R.J. Hanson (1991), An Options Manager for the IMSL Fortran 77 Libraries, Technical Report 9101, IMSL, Houston.
Bischof et al.
Bischof, C., J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, D. Sorensen (1988), LAPACK Working Note #5: Provisional Contents, Argonne National Laboratory Report ANL-88-38, Mathematics and Computer Science.
Bjorck
Bjorck, Ake (1967), Iterative refinement of linear least squares solutions I, BIT, 7, 322‑337.
Bjorck, Ake (1968), Iterative refinement of linear least squares solutions II, BIT, 8, 8‑30.
Boisvert (1984)
Boisvert, Ronald (1984), A fourth order accurate fast direct method for the Helmholtz equation, Elliptic Problem Solvers II, (edited by G. Birkhoff and A. Schoenstadt), Academic Press, Orlando, Florida, 35‑44.
Boisvert, Howe, and Kahaner
Boisvert, Ronald F., Sally E. Howe, and David K. Kahaner (1985), GAMS: A framework for the management of scientific software, ACM Transactions on Mathematical Software, 11, 313‑355.
Boisvert, Howe, Kahaner, and Springmann
Boisvert, Ronald F., Sally E. Howe, David K. Kahaner, and Jeanne L. Springmann (1990), Guide to Available Mathematical Software, NISTIR 90-4237, National Institute of Standards and Technology, Gaithersburg, Maryland.
Blackford et al.
Blackford, L. S., Choi, J., Cleary, A., D'Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. and Whaley, R. C., (1997), ScaLAPACK User’s Guide, Society for Industrial and Applied Mathematics, Philadephia, PA.
Brankin et al.
Brankin, R.W., I. Gladwell, and L.F. Shampine, RKSUITE: a Suite of Runge-Kutta Codes for the Initial Value Problem for ODEs, Softreport 91-1, Mathematics Department, Southern Methodist University, Dallas, Texas, 1991.
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.
Brenner
Brenner, N. (1973), Algorithm 467: Matrix transposition in place [F1], Communication of ACM, 16, 692‑694.
Brent
Brent, R.P. (1971), An algorithm with guaranteed convergence for finding a zero of a function, The Computer Journal, 14, 422‑425.
Brent, Richard P. (1973), Algorithms for Minimization without Derivatives, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
Brigham
Brigham, E. Oran (1974), The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, New Jersey.
Cheney
Cheney, E.W. (1966), Introduction to Approximation Theory, McGraw-Hill, New York.
Cline et al.
Cline, A.K., C.B. Moler, G.W. Stewart, and J.H. Wilkinson (1979), An estimate for the condition number of a matrix, SIAM Journal of Numerical Analysis, 16, 368‑375.
Cody, Fraser, and Hart
Cody, W.J., W. Fraser, and J.F. Hart (1968), Rational Chebyshev approximation using linear equations, Numerische Mathematik, 12, 242‑251.
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.
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.
Crump
Crump, Kenny S. (1976), Numerical inversion of Laplace transforms using a Fourier series approximation, Journal of the Association for Computing Machinery, 23, 89‑96.
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.
de Hoog, Knight, and Stokes
de Hoog, F.R., J.H. Knight, and A.N. Stokes (1982), An improved method for numerical inversion of Laplace transforms. SIAM Journal on Scientific and Statistical Computing, 3, 357‑366.
Demmel et al
Demmel, J.W., Gilbert, J.R., and Li, X.S. (2003), SuperLU User's Guide, University of California, Berkeley, CA, Xerox Corporation.
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., and C.B. Moler, (1977) EISPACK A package for solving matrix eigenvalue problems, Argonne National Laboratory, Argonne, Illinois.
Dongarra, J.J., J.R. Bunch, C.B. Moler, and G.W. Stewart (1979), LINPACK Users’ Guide, SIAM, Philadelphia.
Dongarra, J.J., J. DuCroz, S. Hammarling, R. J. Hanson (1988), An Extended Set of Fortran basic linear algebra subprograms, ACM Transactions on Mathematical Software, 14 , 1‑17.
Dongarra, J.J., J. DuCroz, S. Hammarling, I. Duff (1990), A set of level 3 basic linear algebra subprograms, ACM Transactions on Mathematical Software, 16 , 1‑17.
Draper and Smith
Draper, N.R., and H. Smith (1981), Applied Regression Analysis, second edition, John Wiley & Sons, New York.
Du Croz et al.
Du Croz, Jeremy, P. Mayes, G. and 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 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.
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.
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.
Fabijonas
B. R. Fabijonas,. Algorithm 838: Airy Functions, ACM Transactions on Mathematical Software, Vol. 30, No. 4, December 2004, Pages 491–501.
Fabijonas et al.
B. R. Fabijonas, D. W. Lozier, and F. W. J. Olver Computation of Complex Airy Functions and Their Zeros Using Asymptotics and the Differential Equation, ACM Transactions on Mathematical Software, Vol. 30, No. 4, December 2004, 471–490.
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.
Fox, Hall, and Schryer
Fox, P.A., A.D. Hall, and N.L. Schryer (1978), The PORT mathematical subroutine library, ACM Transactions on Mathematical Software, 4, 104‑126.
Garbow
Garbow, B.S. (1978) CALGO Algorithm 535: The QZ algorithm to solve the generalized eigenvalue problem for complex matrices, ACM Transactions on Mathematical Software, 4, 404‑410.
Garbow et al.
Garbow, B.S., J.M. Boyle, J.J. Dongarra, and C.B. Moler (1972), Matrix eigensystem Routines: EISPACK Guide Extension, Springer-Verlag, New York.
Garbow, B.S., J.M. Boyle, J.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 of Mathematical Software, 14, 163‑170.
Gautschi
Gautschi, Walter (1968), Construction of Gauss-Christoffel quadrature formulas, Mathematics of Computation, 22, 251‑270.
Gautschi and Milovanofic
Gautschi, Walter, and Gradimir V. Milovanofic (1985), Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series, Mathematics of Computation, 44, 177‑190.
Gay
Gay, David M. (1981), Computing optimal locally constrained steps, SIAM Journal on Scientific and Statistical Computing, 2, 186‑197.
Gay, David M. (1983), Algorithm 611: Subroutine for unconstrained minimization using a model/trust-region approach, ACM Transactions on Mathematical Software, 9, 503‑ 524.
Gear
Gear, C.W. (1971), Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey.
Gear and Petzold
Gear, C.W., and Linda R. Petzold (1984), ODE methods for the solutions of differential/algebraic equations, SIAM Journal Numerical Analysis, 21, #4, 716.
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 et al.
Gill, Philip E., and Walter Murray (1976), Minimization subject to bounds on the variables, NPL Report NAC 72, National Physical Laboratory, England.
Gill, Philip E., Walter Murray, and Margaret Wright (1981), Practical Optimization, Academic Press, New York.
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.
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, Gene H., and Charles F. Van Loan (1983), Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland.
Golub, Gene H., and Charles F. Van Loan (1989), Matrix Computations, 2d ed., Johns Hopkins University Press, Baltimore, Maryland.
Golub, Gene H., and Charles F. Van Loan (1996), Matrix Computations, 3rd ed., 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.
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
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, Richard.J. (1990), A cyclic reduction solver for the IMSL Mathematics Library, IMSL Technical Report 9002, IMSL, Houston.
Hanson et al.
Hanson, Richard J., R. Lehoucq, J. Stolle, and A. Belmonte (1990), Improved performance of certain matrix eigenvalue computations for the IMSL/MATH Library, IMSL Technical Report 9007, IMSL, Houston.
Hartman
Hartman, Philip (1964) Ordinary Differential Equations, John Wiley and Sons, New York, NY.
Hausman
Hausman, Jr., R.F. (1971), Function Optimization on a Line Segment by Golden Section, Lawrence Radiation Laboratory, University of California, Livermore.
Hindmarsh
Hindmarsh, A.C. (1974), GEAR: Ordinary differential equation system solver, Lawrence Livermore Laboratory Report UCID30001, Revision 3.
Hull et al.
Hull, T.E., W.H. Enright, and K.R. Jackson (1976), User’s guide for DVERK A subroutine for solving non-stiff ODEs, Department of Computer Science Technical Report 100, University of Toronto.
IEEE
ANSI/IEEE Std 754-1985 (1985), IEEE Standard for Binary Floating-Point Arithmetic, The IEEE, Inc., New York.
IMSL (1991)
IMSL (1991), IMSL STAT/LIBRARY User’s Manual, Version 2.0, IMSL, Houston.
Irvine et al.
Irvine, Larry D., Samuel P. Marin, and Philip W. Smith (1986), Constrained interpolation and smoothing, Constructive Approximation, 2, 129‑151.
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, 545566.
Jenkins, M.A., and J.F. Traub (1970), A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numerische Mathematik, 14, 252‑263.
Jenkins, M.A., and J.F. Traub (1972), Zeros of a complex polynomial, Communications of the ACM, 15, 97‑99.
Kennedy and Gentle
Kennedy, William J., Jr., and James E. Gentle (1980), Statistical Computing, Marcel Dekker, New York.
Kershaw
Kershaw, D. (1982), Solution of tridiagonal linear systems and vectorization of the ICCG algorithm on the Cray-1, Parallel Computations, Academic Press, Inc., 85-99.
Knuth
Knuth, Donald E. (1973), The Art of Computer Programming, Volume 3: Sorting and Searching, Addison-Wesley Publishing Company, Reading, Mass.
Krogh
Krogh, Fred T. (1970), Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation, Math. of Comp. 24, 109, 185-190.
Krogh, Fred T. (2005),
An Algorithm for Linear Programming,
http://mathalacarte.com/fkrogh/pub/lp.pdf, Tojunga, CA.
Lawson et al.
Lawson, C.L., R.J. Hanson, D.R. Kincaid, and F.T. Krogh (1979), Basic linear algebra subprograms for Fortran usage, ACM Transactions on Mathematical Software, 5, 308‑ 323.
Leavenworth
Leavenworth, B. (1960), Algorithm 25: Real zeros of an arbitrary function, Communications of the ACM, 3, 602.
Lehoucq et al.
Lehoucq, R. B., Danny C. Sorenson, and Chao Yang (1998), ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, Philadelphia.
Levenberg
Levenberg, K. (1944), A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics, 2, 164‑168.
Lewis et al.
Lewis, P.A. W., A.S. Goodman, and J.M. Miller (1969), A pseudo-random 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. (1986), On the storage requirement in the out-of-core multifrontal method for sparse factorization. ACM Transactions on Mathematical Software, 12, 249‑264.
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 and Ashcraft
Liu, J., and C. Ashcraft (1987), A vector implementation of the multifrontal method for large sparse, symmetric positive definite linear systems, Technical Report ETA-TR-51, Engineering Technology Applications Division, Boeing Computer Services, Seattle, Washington.
Lyness and Giunta
Lyness, J.N. and G. Giunta (1986), A modification of the Weeks Method for numerical inversion of the Laplace transform, Mathmetics 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.
Marquardt
Marquardt, D. (1963), An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics, 11, 431‑441.
Martin and Wilkinson
Martin, R.S., and J.W. Wilkinson (1968), Reduction of the symmetric eigenproblem Ax = λBx and related problems to standard form, Numerische Mathematik, 11, 99‑119.
Matsumoto and Nishimure
Makoto Matsumoto and Takuji Nishimura, ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, Pages 3–30.
Micchelli et al.
Micchelli, C.A., T.J. Rivlin, and S. Winograd (1976), The optimal recovery of smooth functions, Numerische Mathematik, 26, 279285
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.
More et al.
More, Jorge, Burton Garbow, and Kenneth Hillstrom (1980), User guide for MINPACK-1, Argonne National Labs Report ANL-80-74, Argonne, Illinois.
Muller
Muller, 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 R. Mead (1965), A simplex method for function minimization, Computer Journal 7, 308‑313.
Neter and Wasserman
Neter, John, and William Wasserman (1974), Applied Linear Statistical Models, Richard D. Irwin, Homewood, Ill.
Park and Miller
Park, Stephen K., and Keith W. Miller (1988), Random number generators: good ones are hard to find, Communications of the ACM, 31, 1192‑1201.
Parlett
Parlett, B.N. (1980), The Symmetric Eigenvalue Problem, Prentice‑Hall, Inc., Englewood Cliffs, New Jersey.
Patterson
Patterson, T.N.L, (1968), The Optimum Addition Of Points To Quadrature Formulae. Mathematics of Comp, 22, 847-856.
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, 6788.
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. Uberhuber, and D.K. Kahaner (1983), QUADPACK, Springer-Verlag, New York.
Powell
Powell, M.J.D. (1977), Restart procedures for the conjugate gradient method, Mathematical Programming, 12, 241‑254.
Powell, M.J.D. (1978), A fast algorithm for nonlinearly constrained optimization calculations, in 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. (1983), ZQPCVX a FORTRAN subroutine for convex quadratic programming, DAMTP Report NA17, Cambridge, England.
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 optimization calculations, DAMTP Report NA17, University of Cambridge, England.
Powell, M.J.D. (1989), TOLMIN: A fortran package for linearly constrained optimization calculations, DAMTP Report NA2, University of 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.
Pruess and Fulton
Pruess, S. and C.T. Fulton (1993), Mathematical Software for Sturm-Liouville Problems, ACM Transactions on Mathematical Software, 17, 3, 360376.
Ralston
Ralston, Anthony (1965), A First Course in Numerical Analysis, McGraw-Hill, New York.
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 minimal residual residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 856869.
Schittkowski
Schittkowski, K. (1987), More test examples for nonlinear programming codes, SpringerVerlag, Berlin, 74.
Schnabel
Schnabel, Robert B. (1985), Finite Difference Derivatives Theory and Practice, Report, National Bureau of Standards, Boulder, Colorado.
Schreiber and Van Loan
Schreiber, R., and C. Van Loan (1989), A Storage‑Efficient WY Representation for Products of Householder Transformations, SIAM J. Sci. Stat. Comp., Vol. 10, No. 1, pp. 53-57, January (1989).
Scott et al.
Scott, M.R., L.F. Shampine, and G.M. Wing (1969), Invariant Embedding and the Calculation of Eigenvalues for Sturm-Liouville Systems, Computing, 4, 1023.
Sewell
Sewell, Granville (1982), IMSL software for differential equations in one space variable, IMSL Technical Report 8202, IMSL, Houston.
Sewell, Granville (2005), Computational Methods of Linear Algebra, section 4.6, 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.
Sorensen
Sorensen, D.C. (1992), Implicit Application of Polynomial Filters in a K-step Arnoldi Method, SIAM, J. Matrix Analysis and Applications, 13(1): 357-385.
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, R.C. (1969), Algorithm 347: An efficient algorithm for sorting with minimal storage, Communications of the ACM, 12, 185‑187.
Smith
Smith, B.T. (1967), ZERPOL, A Zero Finding Algorithm for Polynomials Using Laguerre’s Method, Department of Computer Science, University of Toronto.
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.
Spang
Spang, III, H.A. (1962), A review of minimization techniques for non-linear functions, SIAM Review, 4, 357‑359.
Stewart
Stewart, G.W. (1973), Introduction to Matrix Computations, Academic Press, New York.
Stewart, G.W. (1976), The economical storage of plane rotations, Numerische Mathematik, 25, 137‑139.
Stoer
Stoer, J. (1985), Principles of sequential quadratic programming methods for solving nonlinear programs, in Computational Mathematical Programming, (edited by K. Schittkowski), NATO ASI Series, 15, Springer-Verlag, Berlin, Germany.
Stroud and Secrest
Stroud, A.H., and D.H. Secrest (1963), Gaussian Quadrature Formulae, Prentice-Hall, Englewood Cliffs, New Jersey.
Titchmarsh
Titchmarsh, E. Eigenfunction Expansions Associated with Second Order Differential Equations, Part I, 2d Ed., Oxford University Press, London, 1962.
Trench
Trench, W.F. (1964), An algorithm for the inversion of finite Toeplitz matrices, Journal of the Society for Industrial and Applied Mathematics, 12, 515‑522.
Walker
Walker, H.F. (1988), Implementation of the GMRES method using Householder transformations, SIAM J. Sci. Stat. Comput., 9, 152163.
Washizu
Washizu, K. (1968), Variational Methods in Elasticity and Plasticity, Pergamon Press, New York.
Watkins and Elsner
Watkins, D.S., and L. Elsner (1990), Convergence of algorithms of decomposition type for the eigenvalue problem, Linear Algebra and Applications (to appear).
Weeks
Weeks, W.T. (1966), Numerical inversion of Laplace transforms using Laguerre functions, J. ACM, 13, 419‑429.
Wilkinson
Wilkinson, J.H., and Howinson, S., and Dewynne, J (1965), The Algebraic Eigenvalue Problem, Oxford University Press, London, 635.
Wilmot et al.
Wilkinson, J.H. (1965), The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, NY, 41-57.