Gilbert Strang's Bibliography

(also available in latex and postscript )

  1. An improvement on the Holzer table based on a suggestion of Rayleigh's, with S.H. Crandall, J. Appl. Mechanics, Paper 56-A27 (1957).
  2. On the order of convergence of the Crank-Nicolson procedure, J. Math. and Physics 83 (1959) 141-144.
  3. Difference methods for mixed boundary-value problems, Duke Math. Journal 27 (1960) 221-232.
  4. On the Kantorovich inequality, Proc. Amer. Math. Soc., 11 (1960) 468.
  5. A note on the joint spectral radius, with G.-C. Rota, Proc. Netherlands Academy 22 (1960) 379-381.
  6. Finite difference techniques for a boundary problem, with L. Ehrlich, J.  Riley and B.A. Troesch, J. Soc. Ind. Appl. Math. (1961).
  7. Eigenvalues of Jordan products, Amer. Math. Monthly 69 (1962) 37-40.
  8. Trigonometric polynomials and difference methods of maximum accuracy, J. Math. and Phys. 41 (1962) 147-154.
  9. Polynomial approximation of Bernstein type, Trans. Amer. Math. Soc. 105 (1962) 525-535.
  10. Comparison theorems for supremum norms, with H. Schneider, Numerische Math. 4 (1962) 15-20.
  11. Accurate partial difference methods I: Linear Cauchy problems, Arch. Rat. Mech. Anal. 12 (1963).
  12. Accurate partial difference methods II: Non-linear problems, Numerische Math. 6 (1964) 37-46.
  13. Wiener-Hopf difference equations, J. Math. Mechanics 13 (1964) 85-96.
  14. Unbalanced polynomials and difference methods for mixed problems, SIAM J. Numer. Anal. 2 (1964) 46-51.
  15. Necessary and insufficient conditions for well-posed Cauchy problems, J. Diff. Eq. 2 (1966) 107-114.
  16. Matrix theorems for partial differential and difference equations, with J. Miller, Math. Scand. 18 (1966) 113-133.
  17. Implicit difference methods for initial-boundary value problems, J. Math. Anal. Appl. 16 (1966) 188-198.
  18. On strong hyperbolicity, J. Math. Kyoto Univ. 6 (1967) 397-417.
  19. A variant of Caratheodory's problem, Proc. Edinburgh Math. Soc. 16 (1968) 43-48.
  20. The nucleus of a set, Canad. Math. Bull. 11 (1968) 65-72.
  21. On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968) 506-517.
  22. Approximating semigroups and the consistency of difference schemes, Proc. Amer. Math. Soc. 20 (1969) 1-7.
  23. Hyperbolic initial-boundary value problems in two unknowns, J. Diff. Eq. 6 (1969) 161-171.
  24. On numerical ranges and holomorphic semigroups, J. d'Analyse Math. 22 (1969) 299-318.
  25. On multiple characteristics and the Levi-Lax conditions for hyperbolicity, Arch. Rat. Mech. Anal. 33 (1969) 358-373.
  26. Fourier analysis of the finite element method in Ritz-Galerkin theory, with G. Fix, Studies in Appl. Math. 48 (1969) 265-273.
  27. Toeplitz operators in a quarter-plane, Bull. Amer. Math. Soc. 76 (1970) 1303-1307.
  28. The correctness of the Cauchy problem, with H. Flaschka, Advances in Math. 6 (1971) 347-349.
  29. The finite element method and approximation theory, SYNSPADE Proceedings, Academic Press (1971) 547-584.
  30. The change in solution due to change in domain, with A. Berger, AMS Symposium on Partial Differential Equations, Berkeley (1971) 199-206.
  31. Approximation in the finite element method, Numerische Math. 19 (1972) 81-98.
  32. Approximate boundary conditions in the finite element method, with R. Scott and A. Berger, Symposia Mathematica X, Istituto Nationale di Alta Matematica (1972) 295-313.
  33. Variational crimes in the finite element method, ``The Mathematical Foundations of the Finite Element Method'', ed. by A.K. Aziz, Academic Press (1973) 689-710.
  34. A Fourier analysis of the finite element variational method, with G. Fix, Constructive Aspects of Functional Analysis, Edizioni Cremonese, Rome (1973) 795-840.
  35. Piecewise polynomials and the finite element method, AMS Bulletin 79 (1973) 1128-1137.
  36. Optimal conditioning of matrices, with C. McCarthy, SIAM J. Numer. Anal. 10 (1973) 370-388.
  37. The dimension of piecewise polynomial spaces and one-sided approximation, Proc. Conference on Numerical Analysis, Dundee, Springer Lecture Notes 363 (1974) 144-152.
  38. One-sided approximation and plate bending, Lecture Notes in Computer Science 11, Springer-Verlag (1974) 140-155.
  39. One-sided approximation and variational inequalities, with U. Mosco, Bull. Amer. Math. Soc. 80 (1974) 308-312.
  40. The finite element method--linear and nonlinear applications, Proc. Intern. Congress of Mathematicians, Vancouver (1974).
  41. Free boundaries and finite elements in one dimension, with W. Hager, Math. Comp. 29 (1975) 1020-1031.
  42. A homework exercise in finite elements, Inter. J. Num. Meth. in Engineering 11 (1977) 411-418.
  43. Some recent contributions to plasticity theory, J. Franklin Institute 302 (1977) 429-442.
  44. Discrete plasticity and the complementarity problem, Proceedings U.S.-Germany Symposium: Formulations and Computational Algorithms in Finite Element Analysis, M.I.T. Press (1977) 839-854.
  45. Uniqueness in the theory of variational inequalities, Advances in Math. 22 (1976) 356-363.
  46. A minimax problem in plasticity theory, Functional Analysis Methods in Numerical Analysis, ed. M.Z. Nashed, Springer Lecture Notes 701 (1979) 319-333.
  47. A family of model problems in plasticity, Proc. Symp. Computing Methods in Applied Sciences, ed. R. Glowinski and J.L. Lions, Springer Lecture Notes 704 (1979) 292-308.
  48. The saddle point of a differential program, with H. Matthies and E.Christiansen, Energy Methods in Finite Element Analysis, ed. by R. Glowinski, E. Rodin, and O.C. Zienkiewicz, John Wiley (1979).
  49. The solution of nonlinear finite element equations, with H. Matthies, Inter. J. Num. Meth. in Eng. 14 (1979) 1613-1626.
  50. Mathematical and computational methods in plasticity, with H. Matthies and R. Temam, Proc. IUTAM Symp. on Variational Methods in the Mechanics of Solids, S. Nemat- Nasser, ed., Pergamon (1980) 20-28.
  51. Spectral decomposition in advection-diffusion analysis by finite element methods, with R. Nickell and D. Gartling, Proc. FENOMECH Symp., Stuttgart (1978); Computer Methods in Appl. Mech. and Eng. 17 (1979) 561-580.
  52. Existence de solutions relaxées pour les équations de la plasticité, with R. Temam, Comptes Rendus Acad. Sc. Paris 287 (1978) 515-519.
  53. Functions of bounded deformation, with R. Temam, Arch. Rat. Mech. Anal. 75 (1980) 7-21.
  54. Numerical computations in nonlinear mechanics, with H. Matthies, Paper 79-PVP-103, Amer. Soc. Mech. Eng. (1979); Proceedings of the 4th Symposium on Computing Methods in Applied Sciences and Engineering, ed. R. Glowinski and J.L. Lions, 517-525, North-Holland (1980).
  55. Duality and relaxation in the variational problems of plasticity, with R. Temam, J. de Mécanique 19 (1980) 1-35.
  56. The quasi-Newton method in finite element calculations, Chapter 20 in Computational Methods in Nonlinear Mechanics, J.T. Oden, ed., North-Holland (1980).
  57. The application of quasi-Newton methods in fluid mechanics, with M. Engelman and K.J. Bathe, Int. J. Num. Meth. Eng. 17 (1981) 707-718.
  58. A problem in capillarity and plasticity, with R. Temam, Nondifferentiable and Variational Techniques in Optimization, D.C. Sorenson, R.J.B. Wets, eds., Mathematical Programming Study 17 (1982) 91-102.
  59. Optimal design for torsional rigidity, with R. Kohn, Proc. Int. Symp. on Mixed and Hybrid Finite Element Methods, Atlanta (1981).
  60. Optimal design of cylinders in shear, with R. Kohn, MAFELAP Conference, Brunel (1981).
  61. The width of a chair, American Math. Monthly 89 (1982) 529-534.
  62. Structural design optimization, homogenization, and relaxation of variational problems, with R. Kohn, Proceedings of Conference on Disordered Media, Lecture Notes in Physics 154, Springer-Verlag (1982) New York.
  63. Hencky-Prandtl nets and constrained Michell trusses, with R. Kohn, Conference on Optimum Structural Design, Tucson (1981), Computer Methods in Applied Mechanics and Engineering 36 (1983) 207-222.
  64. The optimal accuracy of difference schemes, with A. Iserles, Transactions Amer. Math. Soc. 277 (1983) 770-803.
  65. Duality in the classroom, American Math. Monthly 91 (1984) 250-254.
  66. Maximal flow through a domain, Mathematical Programming 26 (1983) 123-143.
  67. Barriers to stability, with A. Iserles, SIAM J. Numerical Analysis 20 (1983) 1251-1257.
  68. L^1 and L^infty and approximation of vector fields in the plane, ``Nonlinear Partial Differential Equations in Applied Science,'' H. Fujita, P. Lax, and G. Strang, eds., Lecture Notes in Num. Appl. Anal. 5 (1982) 273-288.
  69. Notes on softening and local instability, with M. Abdel-Naby, in ``Computational Aspects of Penetration Mechanics,'' Springer Lecture Notes in Engineering 3, J. Chandra and J. Flaherty, eds. (1983).
  70. A negative results for nonnegative matrices, Journal of Xian Jiaotong University 17 (1983) 69-72.
  71. Numerical and biological shape optimization, with A. Philpott, in ``Unification of Finite Element Methods,'' Math. Studies 94, H. Kardestuncer, ed., North-Holland (1984).
  72. Explicit relaxation of a variational problem in optimal design, with R. Kohn, Bull. Amer. Math. Soc. 9 (1983) 211-214.
  73. Optimal design and relaxation of variational problems, with R. Kohn, Communications on Pure and Appl. Math. 39 (1986) 113-137 (Part I), 139-182 (Part II), 353-377 (Part III).
  74. The constrained least gradient problem, with R. Kohn, in Non-Classical Continuum Mechanics, R. Knops and A. Lacey, eds., Cambridge University Press (1987).
  75. The optimal design of a two-way conductor, with R. Kohn, in Nonsmooth Mechanics, P.D. Panagiotopoulos et al, eds., Birkhäuser (1987).
  76. Fibered structures in optimal design, with R. Kohn, Ordinary and Partial Differential Equations, B. Sleeman and R. Jarvis, eds., Pitman Research Notes 157, Longman (1987).
  77. Optimal design in elasticity and plasticity, with R. Kohn, Int. J. Numerical Meths. in Eng. 22 (1986) 183-188.
  78. A framework for equilibrium equations, SIAM Review 30 (1988) 283-297.
  79. Karmarkar's algorithm in a nutshell, SIAM News 18 (1985) 13.
  80. Karmarkar's algorithm and its place in applied mathematics, Math. Intelligencer 9 (1987) 4-10.
  81. A proposal for Toeplitz matrix calculations, Studies in Appl. Math. 74 (1986) 171-176.
  82. The Toeplitz-circulant eigenvalue problem Ax = lambda Cx, with A. Edelman, pp. 109-117 in Oakland Conf. on PDE's and Applied Mathematics, L. Bragg and J. Dettman, eds., Longman (1987).
  83. Patterns in linear algebra, American Math. Monthly 96 (1989) 105-117.
  84. Paradox lost: Natural boundary conditions in the Ritz- Galerkin method, with J. Storch, Int. J. Numerical Methods in Engineering 26 (1988) 2255-2266.
  85. Dual extremum principles in finite elastoplastic deformation, with Y. Gao, Acta Appl. Mathematicae 17 (1989) 257-268.
  86. Toeplitz equations by conjugate gradients with circulant preconditioner, with R. Chan, SIAM J. Sci. Stat. Comp. 10 (1989) 104-119.
  87. Geometric nonlinearity: Potential energy, complementary energy, and the gap function, with Y. Gao, Quarterly of Applied Mathematics 47 (1989) 487-504.
  88. Teaching modern engineering mathematics, Applied Mechanics Review 39 (1986) 1319-1321; SEFI Proceedings, L. Rade, ed., Chartwell-Bratt (1988).
  89. Sums and differences vs. integrals and derivatives, College Mathematics Journal 21 (1990) 20-27.
  90. Wavelets and dilation equations: A brief introduction, SIAM Review 31 (1989) 614-627.
  91. Inverse problems and derivatives of determinants, Archive Rational Mech. and Analysis 114 (1991) 255-265.
  92. A thousand points of light, with D. Hardin, Third Conference on Technology in Collegiate Mathematics (1990).
  93. A chaotic search for i, College Math. Journal 22 (1991) 3-12.
  94. The optimal coefficients in Daubechies wavelets, Physica D 60 (1992) 239-244.
  95. Polar area is the average of strip areas, Amer. Math. Monthly 100 (1993) 250-254.
  96. The fundamental theorem of linear algebra, Amer. Math. Monthly 100 (1993) 848-855.
  97. Wavelet transforms versus Fourier transforms, Bull. Amer. Math. Soc. 28 (1993) 288-305.
  98. Graphs, matrices, and subspaces, College Math. Journal 24 (1993) 20-28.
  99. The asymptotic probability of a tie for first place, with B. Eisenberg and G. Stengle, Annals of Applied Probability 3 (1993) 731-745.
  100. Continuity of the joint spectral radius: Applications to wavelets, with C. Heil, Linear Algebra for Signal Processing, A. Bojanczyk and G. Cybenko, eds., IMA 69 (1994) Springer-Verlag.
  101. Convolution, reconstruction, and wavelets, Advances in Computational Mathematics: New Delhi, H.P. Dikshit and C.A. Micchelli, eds. (1994), World Scientific Publishing.
  102. Short wavelets and matrix dilation equations, with V. Strela, IEEE Trans. on Signal Processing 43 (1995) 108-115.
  103. Orthogonal multiwavelets with vanishing moments, with V. Strela, Proc. SPIE Conference on Mathematics of Imaging, J. Optical Eng. 33 (1994) 2104-2107.
  104. Wavelets, American Scientist 82 (1994) 250-255.
  105. Every unit matrix is a LULU, Linear Algebra and Its Applications 265 (1997) 165-172.
  106. Finite element multiwavelets, with V. Strela, Proc. Maratea NATO Conference, Kluwer (1995).
  107. Approximation by translates of refinable functions, with C. Heil and V. Strela, Numerische Mathematik 73 (1996) 75-94.
  108. The cascade algorithm for the dilation equation, Proc. Argonne Conference on Wavelets (1994).
  109. Eigenvalues (downarrow 2) and convergence of the cascade algorithm, IEEE Trans. Signal Processing 44 (1996) 233-238.
  110. The applications of multiwavelet filter banks to image processing, with P. Heller, V. Strela, P. Topiwala, and C. Heil, IEEE Trans. Image Processing, 8 (1999) 548-563.
  111. Asymptotic analysis of Daubechies polynomials, with Jianhong Shen, Proc. Amer. Math. Soc. 124 (1996) 3819-3833.
  112. Biorthogonal multiwavelets and finite elements, with V. Strela, preprint (1996).
  113. Condition numbers for wavelets and filter banks, Computational and Appl. Math. (Brasil) 15 (1996) 161-179.
  114. Eigenvalues of Toeplitz matrices with 1 x 2 blocks, Zeit. Angew. Math. Mech. 76 (1996) 37-39.
  115. Asymptotic structures of Daubechies scaling functions and wavelets, with Jianhong Shen, Appl. and Comp. Harmonic Analysis 5 (1998) 312-331.
  116. Wavelets from filter banks, The Mathematics of Numerical Analysis AMS-SIAM Park City Symposium, J. Renegar, M. Shub, and S. Smale, eds. (1996), 765-806.
  117. Filter banks and wavelets, in Wavelets: Theory and Applications, G. Erlebacher, M. Y. Hussaini, L. Jameson, eds., Oxford Univ. Press (1996).
  118. Creating and comparing wavelets, Numerical Analysis: A. R. Mitchell Anniversary Volume, D. Griffiths, ed. (1996).
  119. Writing about mathematics, SIAM News , (June 1996).
  120. The mathematics of GPS, SIAM News , (June 1997).
  121. Wavelets, Iterative Methods in Scientific Computing, pp. 59-110, R. Chan, T. Chan and G. Golub, eds., Springer (1997).
  122. The first moment of wavelet random variables, with Y. Ma and B. Vidakovic, preprint (1997).
  123. The search for a good basis, Numerical Analysis 1997, D. Griffiths, D. Higham, and A. Watson, eds., Addison Wesley Longman (1997).
  124. The asymptotics of optimal (equiripple) filters, with Jianhong Shen, IEEE Trans. on Signal Processing 47 (1999) 1087-1098.
  125. Inhomogeneous refinement equations, with Ding-Xuan Zhou, J.  Fourier Analysis and Applications 4 (1998) 733-747.
  126. Autocorrelation functions in GPS data processing: modeling aspects, with Kai Borre, ION Conference (1997).
  127. A linear algebraic representation of the double entry accounting system, with A. Arya, J. Fellingham, J. Glover, and D. Schroeder, Manuscript (1998).
  128. The discrete cosine transform, block Toeplitz matrices, and filter banks, Computational Mathematics, Shen, Micchelli, Xu, eds. Marcel Dekker (1998).
  129. The discrete cosine transform, SIAM Review 41 (1999) 135-147.
  130. The limits of refinable functions, with Ding-Xuan Zhou, Trans. American Math. Soc 353 (2001) 1971-1984.
  131. The potential theory of several intervals and its applications, with J. Shen and A. Wathen, Appl. Math. Opt. 44 (2001) 67-85.
  132. Row reduction of a matrix and A = CaB, with S. Lee, American Mathematical Monthly 107 (8) October (2000) 681-688.
  133. On wavelet fundamental solutions to the heat equation: Heatlets, with J. Shen, J. Differential Eqns. 161 (2000) 403-421.
  134. Compactly supported refinable functions with infinite masks, with V. Strela and Ding-Xuan Zhou, in The Functional and Harmonic Analysis of Wavelets and Frames, L.Baggett and D.Larson, eds., American Math. Soc. Contemporary Mathematics 247 (1999) 285-296.
  135. Trees with Cantor eigenvalue distribution, with Li He and Xiangwei Liu, submitted to J. Combinatorial Theory (1999).
  136. Eigenstructures of spatial design matrices, with D. Gorsich and M. Genton, to appear in J. Multivariate Analysis (2001).
  137. On the factorization of M-channel paraunitary filter banks, with X.Q. Gao and T. Nguyen, IEEE Transactions on Signal Processing 49 (2001), 1433-1446.
  138. Detection and short-term prediction of epileptic seizures from the EEG signal by wavelet analysis and gaussian mixture model, with Lingmin Meng, Mark Frei, Ivan Osorio, and Truong Nguyen, to appear.
  139. Laplacian eigenvalues of growing trees, with Li He and Xiangwei Liu, Proc. Conf. on Math. Theory of Networks and Systems, Perpignan (2000).
  140. Teaching and learning on the Internet, Mathematical Association of America, to appear (2001)
  141. The joint spectral radius, Commentary by Gilbert Strang on paper # 5 , Collected Works of Gian-Carlo Rota (2001).
  142. Localized eigenvectors from widely spaced matrix modifications, with Xiangwei Liu and Susan Ott, in preparation.
  143. IMACS Matrices, Proceedings of 16th IMACS World Congress (2000).
  144. Signal processing for everyone, Computational Mathematics Driven by Industrial Problems , Springer Lecture Notes in Mathematics 1739 , V. Capasso, H. Engl, and J. Periaux, eds. (2000).
  145. A study of two-channel complex-valued filter banks and wavelets with orthogonality and symmetry properties, with X.Q. Gao and T. Nguyen, IEEE Transactions on Signal Processing. 50 (2002), 824-833.
  146. Binomial matrices, with G. Boyd, C. Micchelli, and D.X. Zhou, Advances in Computational Mathematics. 14 (2001), 379-391.
  147. Tridiagonal matrices and low rank inverse, for submission to SIAM Review (2001).
  148. Block tridiagonal matrices and the Kalman filter, Wavelet Analysis: Twenty Years Developments, D.X. Zhou, ed., World Scientific Press (2002).
  149. Too Much Calculus, SIAM Linear Algebra Activity Group, Newsletter (2002).
  150. Pascal matrices, with Alan Edelman, Amer. Math. Monthly, submitted 2003.
  151. The Laplacian Eigenvalues of a Polygon with Pavel Grinfeld, Computers and Mathematics with Applications, (2003).
  152. A Simple Mesh Generator in MATLAB, with Per-Olof Persson, submitted to SIAM Review, 2003.

    153. Postscript versions of recent wavelet papers are also available separately

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