Appendix C: References

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, 296312.

Akima

Akima, H. (1970), A new method of interpolation and smooth curve fitting based on local procedures, Journal of the ACM, 17, 589602.

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.

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), LINPACK 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), 1029.

Atkinson

Atkinson, Ken (1978), An Introduction to Numerical Analysis, John Wiley & Sons, New York.

Atchison and Hanson

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, 322337.

Bjorck, Ake (1968), Iterative refinement of linear least squares solutions II, BIT, 8, 830.

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, 3544.

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, 313355.

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, 692694.

Brent

Brent, R.P. (1971), An algorithm with guaranteed convergence for finding a zero of a function, The Computer Journal, 14, 422425.

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, 368375.

Cody, Fraser, and Hart

Cody, W.J., W. Fraser, and J.F. Hart (1968), Rational Chebyshev approximation using linear equations, Numerische Mathematik, 12, 242251.

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, 297301.

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, 377403.

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, 8996.

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, 357366.

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 , 117.

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 , 117.

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, 302325.

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, 633641.

Duff et al.

Duff, I.S., A.M. Erisman, and J.K. Reid (1986), Direct Methods for Sparse Matrices, Clarendon Press, Oxford.

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, 122.

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, 7488.

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, 104126.

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, 404410.

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, 163170.

Gautschi

Gautschi, Walter (1968), Construction of Gauss-Christoffel quadrature formulas, Mathematics of Computation, 22, 251270.

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, 177190.

Gay

Gay, David M. (1981), Computing optimal locally constrained steps, SIAM Journal on Scientific and Statistical Computing, 2, 186197.

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, 133.

Golub

Golub, G.H. (1973), Some modified matrix eigenvalue problems, SIAM Review, 15, 318334.

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, 221230.

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 Redish

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, 2941.

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 UCID-30001, 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, 129151.

Jenkins

Jenkins, M.A. (1975), Algorithm 493: Zeros of a real polynomial, ACM Transactions on Mathematical Software, 1, 178189.

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, Numerische Mathematik, 14, 252263.

Jenkins, M.A., and J.F. Traub (1972), Zeros of a complex polynomial, Communications of the ACM, 15, 9799.

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. (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.

Levenberg

Levenberg, K. (1944), A method for the solution of certain problems in least squares, Quarterly of Applied Mathematics, 2, 164168.

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, 136146.

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, 249264.

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, 310325.

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, 313322.

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, 431441.

Martin and Wilkinson

Martin, R.S., and J.W. Wilkinson (1968), Reduction of the symmetric eigenproblem Ax = lBx and related problems to standard form, Numerische Mathematik, 11, 99119.

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, 279-285

Micchelli, C.A., Philip W. Smith, John Swetits, and Joseph D. Ward (1985), Constrained Lp approximation, Constructive Approximation, 1, 93102.

Moler and Stewart

Moler, C., and G.W. Stewart (1973), An algorithm for generalized matrix eigenvalue problems, SIAM Journal on Numerical Analysis, 10, 241256.

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, 208215.

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, 308313.

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, 11921201.

Parlett

Parlett, B.N. (1980), The Symmetric Eigenvalue Problem, PrenticeHall, Inc., Englewood Cliffs, New Jersey.

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.

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, 241254.

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, 144157.

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.

Pruess and Fulton

Pruess, S. and C.T. Fulton (1993), Mathematical Software for Sturm-Liouville Problems, ACM Transactions on Mathematical Software, 17, 3, 360-376.

Reinsch

Reinsch, Christian H. (1967), Smoothing by spline functions, Numerische Mathematik, 10, 177183.

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, 856-869.

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 StorageEfficient 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, 10-23.

Sewell

Sewell, Granville (1982), IMSL software for differential equations in one space variable, IMSL Technical Report 8202, IMSL, Houston.

Shampine

Shampine, L.F. (1975), Discrete least-squares polynomial fits, Communications of the ACM, 18, 179180.

Shampine and Gear

Shampine, L.F. and C.W. Gear (1979), A user's view of solving stiff ordinary differential equations, SIAM Review, 21, 117.

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, 185187.

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, 357359.

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, 137139.

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, 515522.

Walker

Walker, H.F. (1988), Implementation of the GMRES method using Householder transformations,  SIAM J. Sci. Stat. Comput., 9, 152-163.

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, 419429.

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.


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