John Gregory

Department of Mathematics
Southern Illinois University

Curriculum Vita

Selected Papers

Some of the following papers are available as PDF files.

  1. "An approximation theory for elliptic quadratic forms on Hilbert spaces: Application to the eigenvalue problem for compact quadratic forms," Pacific Journal of Mathematics, Volume 37, No. 2, 1970, 383-395, MR43#3878.

  2. "A theory of focal points and focal intervals for an elliptic quadratic form on a Hilbert space," Transactions of the American Mathematical Society, Volume 157, June 1971, 119-128, MR46#2449.

  3. "A theory of numerical approximation for elliptic forms associated with second order differential systems: Application to eigenvalue problems," Journal of Mathematical Analysis and Applications, Volume 38, No. 2, May 1972, 416-426, MR48#1014.

  4. "An approximation theory for focal points and focal intervals," Proceedings of the American Mathematical Society, Volume 32, No. 2, April 1972, 477-487, MR45#5847.

  5. "Numerical focal point and focal interval problems," Journal of Mathematical Analysis and Applications, Volume 41, No. 1, January 1973, 125-131, MR48#1458.

  6. "A new definition of oscillation; application to control and abnormal second differential equations," Journal of Mathematical Analysis and Applications, Volume 43, No. 1, July 1973, 128-135, MR47#8974.

  7. "An approximation theory for oscillations of differential equations," Proceedings of the American Mathematical Society Volume 40, No. 1, September 1973, 166-172, MR48#610.

  8. "An oscillation theory for second order integral differential equations," Journal of Mathematical Analysis and Applications, Volume 47, No. 1, July 1974, 69-78, MR50#3089.

  9. "A numerical oscillation theory for second order integral differential equations," Journal of Mathematical Analysis and Applications, Volume 47, No. 2, August 1974, 227-232, MR50#3090.

  10. J. Gregory and F. Richards, "Numerical approximation for 2nth order differential systems via splines," Rocky Mountain Journal of Mathematics, Volume 5, No. 1, Winter 1975, MR52#9624.

  11. "Elliptic quadratic forms, focal points and a generalized theory of oscillation," Journal of Mathematical Analysis and Applications, Volume 51, No. 3, September 1975, 580-595, MR51#8933.

  12. J. Gregory and G.C. Lopez, "An approximation theory for generalized Fredholm quadratic forms and integral differential equations," Transactions of the American Mathematical Society, Volume 222, 1976, 319-335, MR54#11008.

  13. "Comparison theorems for oscillation of nonlinear, nonselfadjoint equations by use of quadratic forms," Journal of Mathematical Analysis and Applications, Volume 57, No. 3, March 1, 1977, 676-682, MR56#8971.

  14. "Before bifurcation and nonlinearity: numerical solutions of linear problems," Proceedings of the Symposium on Dynamical Systems, (Gainesville, Florida), Academic Press, (Asori, Ed.), 1977, 419-422.

  15. "Numerical Algorithms for oscillation vectors of Lagrange equations for Symmetric Tridiagonal Matrices," Pacific Journal of Mathematics, Volume 76, No. 2, June 1978, 387-406, 58#19161.

  16. J. Gregory and R. Wilkerson, "New numerical methods for symmetric differential equations, quadratic extremal problems and banded matrices; the second order problem," Transactions of the Illinois State Academy of Science, Volume 71, No. 2, (1978), 222-235, MR80h:65069(A.R.).

  17. "Generalized Fredholm quadratic forms and integral differential equations of the second kind," Journal of Mathematical Analysis and Applications, Volume 70, No. 1, July 1979, 120-130, 80j:45014.

  18. J. Gregory and R. Wilkerson, "New numerical algorithms for eigenvalues and eigenvectors of second order differential equations," Journal of Applicable Analysis, 1981, Vol. 12, pp. 47-56.

  19. J. Gregory and R. Wilkerson, "The double eigenvalue problem; including numerical solutions," Journal of Mathematical Analysis and Applications, Volume 83, No. 2, October 1981, 438-44.

  20. J. Gregory and Charles Gibson, "Cheap shooting methods for self-adjoint problems using initial value methods," Proceedings of the International Conference on Nonlinear Phenomena in Mathematical Sciences (Arlington, Texas), Academic Press, 1982, 451-462.

  21. John Gregory, Marvin Zeman, and Charles Gibson, An Initial Value, Finite Element Method, Proceedings of the International Symposium on Dynamical Systems, II (Gainsville, FL), Academic Press, 1982, 535-538.

  22. John Gregory and Ralph Wilkerson, An Approximation Theory for Conjugate Surfaces and Solutions of Elliptic Multiple Integral Problems; Application to Numerical Solutions of Generalized Laplace's Equation, Journal of Mathematical Analysis and Applications, Volume 88, No. 1, July 1982, 231-244.

  23. John Gregory and Don Redmond, A New Look at the Eigenvalue Problem for Real Symmetric Matrices, Transactions of the Illinois State Academy of Sciences, Volume 76, No. 1, 1983, 153-160.

  24. John Gregory and Charles Gibson, Numerical Algorithms for Second Order Systems; Applications to Higher Order Conjugate Points and Eigenvalue Problems, Applicable Analysis, Volume 14, No. 3, 1983, 213-221.

  25. John Gregory and Marvin Zeman, An Optimal L Error Estimate for Galerkin Approximations to Solutions of Two-point Nonlinear Boundary Value Problems, Proceedings of the Vth International Conference in Theory and Practice of Nonlinear Differential Equations, Marcel Dekker, Inc., 1984, 201-206.

  26. John Gregory and Marvin Zeman, A Galerkin Approximation for the Initial-Value Problem for Linear Second Order Differenial Equations, Applied Mathematics and Computation, Elsevier Science Publishing Co., Inc., Volume 15, 1984, 93-108.

  27. John Gregory, Marvin Zeman, and Mohsen Badiey, A Finite Element Approximation for the Initial-Value Problem for Nonlinear Second Order Differential Equations, Journal of Mathematical Analysis and Applications, Volume 111, No. l, October 1985, 90-104.

  28. John Gregory, Marvin Zeman, and Mohsen Badiey, A Finite Element Approximation for the Initial-Value Problem for Nonlinear Second Order Differential Equations II: Systems, Journal of Mathematical Analysis and Applications, Volume 115, No. 1, April 1986.

  29. John Gregory and Marvin Zeman, Some Higher Order Methods for Boundary Value Problems for Second Order Nonlinear Differential Equations, in Qualitative Properties of Differential Equations, ed. by W. Allegretto and G.J. Butler, Edmonton, 1986, 170-178.

  30. Rohan Dalpatadu and John Gregory, Numerical Methods for Optimal Control Problems with Bilinear Objective Functionals and Linear Trojectories, in Current Trends in Matrix Theory, ed. by F. Uhlig and R. Grone, Elsevier Science Publishing Company, 1987, 89-101.

  31. Rohan Dalpatadu and John Gregory, Efficient Numerical Methods for Optimal Control Problems via the Calculus of Variations, Proceedings of the VIIth International Conference on Nonlinear Analysis and Applications, Marcel Dekker, Inc., 1987, 139-147.

  32. John Gregory and Marvin Zeman, Spline Matrices and Their Applications to Some Higher Order Methods for Boundary Value Problems, SIAM Journal of Numerical Analysis, Vol. 25, No. 2, April 1988, 399-410.

  33. John Gregory, Tejendra Sarker and Marvin Zeman, Higher Order Discretization Methods for y" = f(x, y, y'), Journal of Mathematical Analysis and Applications, Volume 136, No. 1, 1988, 141-156.

  34. Numerical Methods for External Problems in the Calculus of Variations and Optimal Control Theory, Bulletin (New Series) of the American Mathematical Society, Volume 18, No. 1, January 1988, 31-34.

  35. John Gregory and Cantian Lin, Efficient General Numerical Methods in Optimal Control Theory, Modern Optimal Control, Marcel Dekker, Inc., 1989, 115-129.

  36. John Gregory and Rong Sheng Wang, New Efficient Methods for the Numerical Solution of Extremaloid Solutions in the Calculus of Variations, Indianapolis Journal of Mathematics and Physics, Volume 3, 1989, 84-107.

  37. John Gregory and Rong Sheng Wang, Discrete Variable Methods for the m-Dependent Variable, Nonlinear External Problem in the Calculus of Variations, SIAM Journal of Numerical Analysis, Vol. 27, No.2, April 1990, 470-487.

  38. John Gregory, Cantian Lin and Rong Sheng Wang, Numerical Extremal Methods and Biological Models, Rocky Mountain Journal of Mathematics, Vol. 20, Issue #4 (Fall 1990), 933-945.

  39. John Gregory and Cantian Lin, The Numerical Solution of Variable Endpoint Problems in the Calculus of Variations, Differential Equations: Stability and Control, Marcel Dekker, 1990, 175-183.

  40. John Gregory and Cantian Lin, Numerical Transversality Conditions in Optimization Problems, Congressus Numerantium, Volume 71, 1990, 87-94.

  41. John Gregory and Cantian Lin, Numerical Solution of Optimal Control Problems with Bounded State Constraints, Congressus Numerantium, Volume 77, 1990, 153-156.

  42. Rohan Dalpatadu, Charles Gibson and John Gregory, Numerical Methods for Nonlinear Optimal Control Problems: Application to Abnormal Problems, Journal of Mathematical Analysis and Applications, Volume 159, No. 1, July 15, 1991.

  43. John Gregory and Cantian Lin, Explicit Kuhn-Tucker Conditions for Optimal Control/Calculus of Variation Problems, Congressus Numeratium, Volume 81, 1991, 81-88.

  44. John Gregory, Robert Gregory, Cantian Lin, and Marvin Zeman, A Global 0(h 4 ) Pointwise Error Numerical Algorithm for the Extremal Solution in the Calculus of Variations, Congressus Numerantium, Volume 86, March 1992, 129-147.

  45. John Gregory and Cantian Lin, Discrete Variable Methods for the m-dependent Variable, Nonlinear Extremal Problem in the Calculus of Variations, II, SIAM Journal of Numerical Analysis, Vol. 30, No. 3, June 1993, 871-883.

  46. John Gregory and Cantian Lin, An Unconstrained Calculus of Variations Formulation for Generalized Optimal Control Problems and for the Constrained Problem of Bolza, Journal of Mathematical Analysis and Applications, Vol. 187, No. 3, 1994, 826-841.

  47. John Gregory and Cantian Lin, Discrete Variable Methods for Nonlinear Extremal Problems Involving Partial Differential Equations, Utilitas Mathematica, Vol. 46, 1994, 103-116.

  48. John Gregory and H.R. Hughes, Random Quadratic Forms, Transactions of the American Mathematical Society, Vol. 347, No. 2, 1995, 709-717.

  49. John Gregory and H.R. Hughes, A Generalized Approximation Theory for Quadratic Forms: Application in Randomized Spline-Type Sturm-Liouville Problems, Journal of Theoretical Probability, Vol. 8, No. 3, 1995, 708-716.

  50. John Gregory and H.R. Hughes, A Generalized Approximation Theory for Quadratic Forms II: Application to Randomized Spline Type Focal/Conjugate Point Problems, Journal of Theoretical Probability, Vol. 8, No. 4, 1995, 963-971.

  51. Om Prakash Agrawal, John Gregory, and Kathleen Pericak-Spector, A Bliss-Type Multiplier Rule for Constrained Variational Problems with Time Delay, J. Math. Analysis & Appl. 210, 1997, 702-711.

  52. John Gregory and Dean Banerjee, New General Analytic and Numerical Methods in Constrained Optimization with Applications to Optimal Consumption, Utilitas Mathematica, 52, 1997, 123-128.

  53. John Gregory and Cantian Lin, Numerical Solutions of Nonlinear Programming Problems with Inequality Constraints by Reformulation, Utilitas Mathematica, 54, Nov. 1998, 252-256.

  54. Om Prakash Agrawal and John Gregory, The Complete Solution for Constrained Delay Problems in the Calculus of Variations by Unconstrained Methods, J. Math. Analysis & Appl., 218, 1998, 127-135.

  55. John Gregory and George Wang, A C Numerical Method for the Basic Problem in the Calculus of Variations, Utilitas Mathematica, 56, Nov. 1999, 79-95.

  56. John Gregory and Kathleen Pericak-Spector, A Bliss-Type Multiplier Rule for Constrained Variational Problems in PDES, Utilitas Mathematica, 56, Nov. 1999, 143-151.

  57. John Gregory and Kathleen Pericak-Spector, New Methods of Solving General Constrained Calculus of Variations Problems Involving PDES, Utilitas Mathematica, 58, Nov. 2000, 215-224.

  58. John Gregory and Matthew Peters, On the Solution of Constrained Wave Equation Problems as an Example of Constrained Energy Laws, Utilitas Mathematica, 59, May 2001, 67-76.

  59. John Gregory and H.R. Hughes, New General Methods for Numerical Stochastic Differential Equations, Utilitas Mathematica, 63, May 2003, 53-64.

  60. Om Prakash Agrawal and John Gregory, A Complete Solution for Optimal Control Delay Problems, Utilitas Mathematica, 64, Nov. 2003, 129-138.

  61. Om Prakash Agrawal and John Gregory, O(h2) Global, Pointwise Algorithms for Delay Linear Regulator Problems in Constrained Optimal Control/Calculus of Variations, SIAM J. of Numerical Analysis, Vol. 41, No. 5, 2004, 1773-1784.

  62. John Gregory and H.R. Hughes, A New Theory and the Efficient Methods of Solution of Strong, Pathwise, Stochastic Variational Problems, Methods and Applications of Analysis, Vol. 11, No. 3, September 2004, 303-316.

  63. John Gregory and H.R. Hughes, Efficient Constrained Optimization: From the Deterministic Past to the Stochastic Future, Nonlinear Analysis, 63, 2005, 763-774.

  64. John Gregory and H.R. Hughes, New Efficient Numerical Procedures for Solving Stochastic Variational Problems with a Priori Maximum Pointwise Error Estimates, accepted for publication, J. Math. Analysis & Appl., 328, 2007, 1378-1395.

  65. John Gregory and H.R. Hughes, The Efficient Solution of the (Quietly Constrained) Noisy, Linear Regulator Problem, accepted for publication and to appear in J. Math. Analysis & Appl.

  66. John Gregory and H.R. Hughes, New Serendipitous Methods for Numerical Solutions of Strong, Pathwise, Stochastic Control Problems, submitted for publication.

  67. John Gregory, A New Systematic Method for Efficiently Solving Holonomic (and Nonholonomic) Constraint Problems, submitted for publication.

  68. John Gregory, Averaging and Bounding Holonomic Constraints: Applications to "Unsolvable" Pendulum Problems, submitted for publication.

  69. John Gregory and H.R. Hughes, Generalizing the Classical Two-Point Boundary Value Problem to O(h2) Global Estimates for the Minimal Variational Problem, submitted for publication.

  70. John Gregory and Gaio Lakin, Simplifying and Reducing the Number of Dependent Variables for Constraint Optimization Problems, accepted for publication and to appear in Applied Mathematical Sciences.

  71. John Gregory, Generalizing Variational Theory to Include the Indefinite Integral, Higher Derivatives, and a Variety of Means as Cost Variables, submitted for publication.

  72. B. Bhattacharya and John Gregory, A General Maximum Entropy Theory: Constraint Optimization in Probability, accepted for publication and to appear in Journal of Computational Mathematics and Optimization.

  73. J. Gregory and G. Lakin, A O(h^2) Global, Numerical Algorithm for Reduced Constraint Optimization Problems.

Home Page: http://www.math.siu.edu/gregory/

E-mail: jgregory@math.siu.edu


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