Publications

Publications by G M Phillips



BOOKS
    G M Phillips and P J Taylor. 'Theory and Applications of Numerical Analysis' Second Edition, Academic Press, 1996 (447 pages).
    G M Phillips and P J Taylor. 'Computers', Methuen, 1969 (178 pages).


REFEREED PAPERS IN JOURNALS AND CONFERENCE PROCEEDINGS
    1. G M Phillips. A property of the axioms of projective geometry. Mathematical Gazette 45, 228-229 (1961).

    2. J Dawson, G M Phillips and B A M Willcox. Computation of X-ray diagnostic exposure tables. Br. J. Radiol. 39, 117-121 (1966).

    3. G M Phillips. Numerical integration in two and three dimensions. Comp. J. 10, 202-204 (1967).

    4. G M Phillips. Numerical integration over an N-dimensional rectangular region. Comp. J. 10, 297-299 (1967).

    5. G M Phillips. Estimate of the maximum error in best polynomial approximations. Comp. J. 11, 110-111 (1968).

    6. G M Phillips. Algorithms for piecewise straight line approximations. Comp. J. 11, 211-212 (1968).

    7. G M Phillips and M A Wolfe. Some methods for the solution of non-singular Volterra integro-differential equations. Comp. J. 11, 334-336 (1968).

    8. G M Phillips. Error estimates for best polynomial approximations. Contrib. to Proceedings of Symposium on Approximation Theory, Lancaster 1969, Academic Press, A Talbot (Ed.), 1-6 (1970).

    9. G M Phillips and P J Taylor. Approximation of convex data. BIT 10, 324-332 (1970).

    10. G M Phillips. Analysis of numerical iterative methods for solving integral and integro-differential equations. Comp. J. 13, 297-299 (1970).

    11. G M Phillips. An error estimate for Volterra integral equations. BIT 11, 181-186 (1971).

    12. G M Phillips. Error estimates for certain integration rules on the triangle. Conference on Applications of Numerical Analysis, Dundee 1971, Lecture Notes in Mathematics 228, 321-326, Springer-Verlag (1971).

    13. A R Mitchell, G M Phillips and E L Wachspress. Forbidden shapes in the finite element method. Journal Inst. Maths. Applications 8, 260-269 (1971).

    14. A R Mitchell and G M Phillips. Construction of basis functions in the finite element method. BIT 12, 81-89 (1972).

    15. G M Phillips. Gregory's method for numerical integration. Amer. Math. Monthly 79, 270-274 (1972).

    16. B H Laidlaw and G M Phillips. Iterative methods for solving Fredholm integral equations. BIT 12, 188-193 (1972).

    17. G M Phillips. Explicit forms for certain Hermite approximations. BIT 13, 177-180 (1973).

    18. J H McCabe and G M Phillips. On a certain class of Lebesgue constants. BIT 13, 434-442 (1973).

    19. F Deutsch, J H McCabe and G M Phillips. Some algorithms for computing best approximations from convex cones. S.I.A.M. Journal of Numerical Analysis 12, 390-403 (1975).

    20. G M Phillips and B N Sahney. An error estimate for least squares approximation. BIT 15, 426-430 (1975).

    21. G M Phillips and B N Sahney. Best simultaneous approximation in the L1 and L2 norms. Contrib. to Theory of Approximation with Applications, Academic Press, 213-219 (1976).

    22. A S B Holland, J H McCabe, G M Phillips and B N Sahney. Best simultaneous L1 approximations. J. Approx. Theory 24, 361-365 (1978).

    23. E W Cheney, J H McCabe and G M Phillips. On simultaneous Chebyshev approximation. J. Approx. Theory 27, 93-98 (1979).

    24. E W Cheney, J H McCabe and G M Phillips. A mixed norm bivariate approximation problem with applications to Lewanowicz operators. Proceedings of the Research Symposium on Multivariate Approximation, University of Durham, 315-323 (1979).

    25. G M Phillips. Best polynomial approximations: a corrected proof. BIT 19, 95-97 (1979).

    26. G M Phillips. Seventh degree integration rules for the cube. BIT 19, 98-103 (1979).

    27. G M Phillips. Seventh degree integration rules for the sphere. BIT 20, 117-119 (1980).

    28. G M Phillips. The development of logarithms. Bull. I.M.A. 16, 165-168 (1980).

    29. G M Phillips. A survey of one-dimensional and multidimensional numerical integration. Comp. Phys. Comm. 20, 17-27 (1980).

    30. R E Grundy and G M Phillips. Application of Hermite approximation to a boundary value problem. J. Comp. Phys. 38, 251-256 (1980).

    31. A S B Holland, G M Phillips and P J Taylor. Generalization of a theorem of Bernstein. Contrib. to Approximation Theory III, Academic Press, E W Cheney (Ed.), 513-516 (1980).

    32. G M Phillips. The summing of square roots. Mathematical Gazette 65, 132-134 (1981).

    33. G M Phillips. Seventh degree integration rules for R3. BIT 21, 126-128 (1981).

    34. G M Phillips. Archimedes the numerical analyst. Amer. Math. Monthly 88, 165-169 (1981).

    35. E W Cheney, W Light, J H McCabe and G M Phillips. The approximation of bivariate functions by sums of univariate ones using the L1 metric. Proc. Edin. Math. Soc. 25, 173-181 (1982).

    36. G M Phillips and P J Taylor. Polynomial approximation using equioscillation on the extreme points of Chebyshev polynomials. J. Approx. Theory 36, 257-264 (1982).

    37. G M Phillips. Rational approximations: a basic approach. Mathematical Gazette 67, 247-250 (1983).

    38. D M E Foster and G M Phillips. A generalization of the Archimedean double sequence. J. Math. Anal. and Applics. 101, 575-581 (1984).

    39. D M E Foster and G M Phillips. The Arithmetic-Harmonic Mean. Math. of Comp. 42, 183-191 (1984).

    40. G M Phillips. Archimedes and the complex plane. Amer. Math. Monthly 91, 108-114 (1984).

    41. G E Bell and G M Phillips. Aitken acceleration of some alternating series. BIT 24, 70-77 (1984).

    42. G M Phillips. Aitken sequences and Fibonacci numbers. Amer. Math. Monthly 91, 354-357 (1984).

    43. A S B Holland, G M Phillips and P J Taylor. A relation between Peano kernels and a theorem of Bernstein. J. Approx. Theory 41, 386-389 (1984).

    44. D M E Foster and G M Phillips. The approximation of certain functions by compound means. Contrib. to NATO Study Institute on Approximation Theory and Spline Functions, D Reidel, 89-95 (1984).

    45. G M Phillips and P J Taylor. Semi-norms in polynomial approximation. Contrib. to NATO Study Institute on Approximation Theory and Spline Functions, D Reidel, 147-150 (1984).

    46. G M Phillips and P J Taylor. On the estimation of orthogonal coefficients. Contrib. to Constructive Theory of Functions 1984, Publishing House of the Bulgarian Academy of Sciences, Sofia, 675-678 (1984).

    47. J H McCabe and G M Phillips. Aitken sequences and generalized Fibonacci numbers. Math. of Comp. 45, 553-558 (1985).

    48. D M E Foster and G M Phillips. General compound means. Contrib. to Approximation Theory and Applications, Research Notes in Mathematics, Pitman, S P Singh (Ed.), 56-65 (1985).

    49. J H McCabe and G M Phillips. Fibonacci and Lucas numbers and Aitken acceleration. Contrib. to Fibonacci Numbers and their Applications, G E Bergum, A N Philippou and A F Horadam (Eds.), D Reidel, 181-184 (1986).

    50. H T Freitag and G M Phillips. A congruence relation for certain recursive sequences. Fibonacci Quarterly 24, 332-335 (1986).

    51. D M E Foster and G M Phillips. Double mean processes. Bull. I.M.A. 22, 170-173 (1986).

    52. G M Phillips. Two topics from the history of numerical analysis in China and Europe. Tianjin Mathematical Journal 4, 47-50 (1986) - in Chinese.

    53. D Elliott, D F Paget, G M Phillips and P J Taylor. Error of truncated Chebyshev series and other near minimax polynomial approximations. J. Approx. Theory 50, 49-57 (1987).

    54. S L Lee and G M Phillips. Interpolation on the triangle. Comm. in Applied Numerical Methods 3, 271-276 (1987).

    55. B L Chalmers, G M Phillips and P J Taylor. Polynomial approximation using projections whose kernels contain the Chebyshev polynomials. J. Approx. Theory 53, 321-334 (1988).

    56. S L Lee and G M Phillips. Interpolating polynomials on the triangle. Contrib. to Constructive Theory of Functions 1987, Publishing House of the Bulgarian Academy of Sciences, Sofia, 288-291 (1988).

    57. S L Lee and G M Phillips. Polynomial interpolation at points of a geometric mesh on a triangle. Proc. Roy. Soc. Edin. 108A, 75-87 (1988).

    58. H T Freitag and G M Phillips. A congruence relation for a linear recursive sequence of arbitrary order. Contrib. to Applications of Fibonacci Numbers, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht-Boston, 39-44 (1988).

    59. S L Lee and G M Phillips. Interpolation on the simplex by homogeneous polynomials. Contrib. to Proceedings of International Conference on Numerical Mathematics, International Series of Numerical Mathematics 86, Birkhäuser Verlag, Basel, 295-305 (1988).

    60. S L Lee and G M Phillips. A recurrence relation for Gaussian multinomial coefficients. Contrib. to Applications of Fibonacci Numbers 3, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht-Boston, 239-240 (1990).

    61. D Elliott and G M Phillips. Improved error bounds for near-minimax approximations, BIT 31, 262-275 (1991).

    62. S L Lee and G M Phillips. Construction of lattices for Lagrange interpolation in projective space, Constructive Approximation 7, 283-297 (1991).

    63. H T Freitag and G M Phillips. On co-related sequences involving generalized Fibonacci numbers, Contrib. to Applications of Fibonacci Numbers 4, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht-Boston, 121-125 (1991).

    64. G M Phillips. Error estimates for near-minimax approximations. Contrib. to Approximation Theory, Spline Functions and Applications, S P Singh (Ed.), Kluwer, Dordrecht-Boston, 223-241 (1992).

    65. G M Phillips and P J Taylor. Algorithms for spline and other approximations to functions and data, Comp. Phys. Comm. 73, 1-21 (1992).

    66. G M Phillips. More applicable error estimates for quadrature rules, Constructive Theory of Functions, Varna 1991, Publishing House of the Bulgarian Academy of Sciences, Sofia, 215-218 (1992).

    67. S L Lee and G M Phillips. Pencils, Pappus' Theorem and Polynomial Interpolation, Math. Medley 20, 68-78 (1992).

    68. H T Freitag and G M Phillips. Co-related sequences satisfying the general second order recurrence relation. Contrib. to Applications of Fibonacci Numbers 5, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht, 257-262 (1993).

    69. D K Dimitrov and G M Phillips. A note on convergence of Newton interpolating polynomials. J. Computational and Applied Math. 51, 127-130 (1994).

    70. Z F Koçak and G M Phillips. B-splines with geometric knot spacings. BIT 34, 388-399 (1994).

    71. S L Lee and G M Phillips. Interpolation on the triangle and simplex. Contrib. to Approximation Theory, Wavelets and Applications, S P Singh, Antonio Carbone and B Watson (Eds.), Kluwer, Dordrecht, 177-196 (1995).

    72. Z F Koçak and G M Phillips. A one-parameter class of B-splines. Contrib. to Approximation Theory, Wavelets and Applications, S P Singh, Antonio Carbone and B Watson (Eds.), Kluwer, Dordrecht, 169-176 (1995).

    73. H T Freitag and G M Phillips. On the sum of consecutive squares. Contrib. to Applications of Fibonacci Numbers 6, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht, 137-142 (1996).

    74. Z F Koçak and G M Phillips. An identity involving the q-factorial. Contrib. to Applications of Fibonacci Numbers 6, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht, 291-296 (1996).

    75. G. M. Phillips. On generalized Bernstein polynomials. Contrib. to Numerical Analysis : A R Mitchell 75th Birthday Volume, D F Griffiths and G A Watson (Eds.), World Scientific, 263-269 (1996).

    76. A Sri Ranga, E X L de Andrade and G M Phillips. Associated symmetric quadrature rules. Applied Num. Math. 21, 175-183 (1996).

    77. H T Freitag and G M Phillips. On the Zeckendorf form of F_{kn}/F_n . Fibonacci Quarterly 34, 444-446 (1996).

    78. G M Phillips. A de Casteljau algorithm for generalized Bernstein polynomials. BIT 36, 232-236 (1996).

    79. G M Phillips. Bernstein polynomials based on the q-integers. Contrib. to The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin, Annals of Numerical Math. 1-4, 511-518 (1997).

    80. G M Phillips. Archimedes the Numerical Analyst. Contrib. to "Pi : A Source Book", L B Berggren, J M Borwein, P B Borwein (Eds.), Springer, 1997.

    81. H T Freitag and G M Phillips. Zeckendorf arithmetic. Contrib. to Applications of Fibonacci Numbers 7, G E Bergum, A N Philippou and A F Horadam (Eds.), Kluwer, Dordrecht (to appear).

    82. G M Phillips. On generalized Bernstein polynomials. Contrib. to Proc. International Conference on Approximation and Optimization, D D Stancu, G Coman, W W Breckner, P Blagu (Eds.), Transylvania Press, 1997.

    83. Z F Koçak and G M Phillips. B-splines with knots spaced in geometric progression. Contrib. to International Conference on Approximation and Optimization, D D Stancu, G Coman, W W Breckner, P Blagu (Eds.), Transylvania Press, 1997.

    84. Tim N T Goodman, Halil Oruç and G M Phillips. Convexity and generalized Bernstein polynomials, Proc. Edin. Math. Soc. (to appear).

    85. Halil Oruç and G M Phillips. A generalization of the Bernstein polynomials, Proc. Edin. Math. Soc. (to appear).



EDITING
    Translation editor of "The Averaged Moduli of Smoothness", B Sendov and V Popov, Wiley, 1988. (Translated from Bulgarian.)