Gilbert Strang's Bibliography
(also available in
latex and
postscript )
- An improvement on the Holzer table based on a suggestion of Rayleigh's,
with S.H. Crandall, J. Appl. Mechanics, Paper 56-A27 (1957).
- On the order of convergence of the Crank-Nicolson procedure, J.
Math. and Physics 83 (1959) 141-144.
- Difference methods for mixed boundary-value problems, Duke Math.
Journal 27 (1960) 221-232.
- On the Kantorovich inequality, Proc. Amer. Math. Soc., 11
(1960) 468.
- A note on the joint spectral radius, with G.-C. Rota, Proc. Netherlands
Academy 22 (1960) 379-381.
- Finite difference techniques for a boundary problem, with L. Ehrlich,
J. Riley and B.A. Troesch, J. Soc. Ind. Appl. Math. (1961).
- Eigenvalues of Jordan products, Amer. Math. Monthly 69
(1962) 37-40.
- Trigonometric polynomials and difference methods of maximum accuracy,
J. Math. and Phys. 41 (1962) 147-154.
- Polynomial approximation of Bernstein type, Trans. Amer. Math. Soc.
105 (1962) 525-535.
- Comparison theorems for supremum norms, with H. Schneider, Numerische
Math. 4 (1962) 15-20.
- Accurate partial difference methods I: Linear Cauchy problems, Arch.
Rat. Mech. Anal. 12 (1963).
- Accurate partial difference methods II: Non-linear problems, Numerische
Math. 6 (1964) 37-46.
- Wiener-Hopf difference equations, J. Math. Mechanics 13
(1964) 85-96.
- Unbalanced polynomials and difference methods for mixed problems, SIAM
J. Numer. Anal. 2 (1964) 46-51.
- Necessary and insufficient conditions for well-posed Cauchy problems,
J. Diff. Eq. 2 (1966) 107-114.
- Matrix theorems for partial differential and difference equations,
with J. Miller, Math. Scand. 18 (1966) 113-133.
- Implicit difference methods for initial-boundary value problems, J.
Math. Anal. Appl. 16 (1966) 188-198.
- On strong hyperbolicity, J. Math. Kyoto Univ. 6 (1967)
397-417.
- A variant of Caratheodory's problem, Proc. Edinburgh Math. Soc.
16 (1968) 43-48.
- The nucleus of a set, Canad. Math. Bull. 11 (1968) 65-72.
- On the construction and comparison of difference schemes, SIAM J.
Numer. Anal. 5 (1968) 506-517.
- Approximating semigroups and the consistency of difference schemes,
Proc. Amer. Math. Soc. 20 (1969) 1-7.
- Hyperbolic initial-boundary value problems in two unknowns, J. Diff.
Eq. 6 (1969) 161-171.
- On numerical ranges and holomorphic semigroups, J. d'Analyse Math.
22 (1969) 299-318.
- On multiple characteristics and the Levi-Lax conditions for hyperbolicity,
Arch. Rat. Mech. Anal. 33 (1969) 358-373.
- Fourier analysis of the finite element method in Ritz-Galerkin theory,
with G. Fix, Studies in Appl. Math. 48 (1969) 265-273.
- Toeplitz operators in a quarter-plane, Bull. Amer. Math. Soc.
76 (1970) 1303-1307.
- The correctness of the Cauchy problem, with H. Flaschka, Advances
in Math. 6 (1971) 347-349.
- The finite element method and approximation theory, SYNSPADE Proceedings,
Academic Press (1971) 547-584.
- The change in solution due to change in domain, with A. Berger,
AMS Symposium on Partial Differential Equations, Berkeley (1971)
199-206.
- Approximation in the finite element method, Numerische Math.
19 (1972) 81-98.
- 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.
- 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.
- A Fourier analysis of the finite element variational method, with G. Fix,
Constructive Aspects of Functional Analysis, Edizioni Cremonese,
Rome (1973) 795-840.
- Piecewise polynomials and the finite element method, AMS Bulletin
79 (1973) 1128-1137.
- Optimal conditioning of matrices, with C. McCarthy, SIAM J.
Numer. Anal. 10 (1973) 370-388.
- The dimension of piecewise polynomial spaces and one-sided approximation,
Proc. Conference on Numerical Analysis, Dundee, Springer Lecture
Notes 363 (1974) 144-152.
- One-sided approximation and plate bending, Lecture Notes in Computer
Science 11, Springer-Verlag (1974) 140-155.
- One-sided approximation and variational inequalities, with U. Mosco,
Bull. Amer. Math. Soc. 80 (1974) 308-312.
- The finite element method--linear and nonlinear applications, Proc.
Intern. Congress of Mathematicians, Vancouver (1974).
- Free boundaries and finite elements in one dimension, with W. Hager,
Math. Comp. 29 (1975) 1020-1031.
- A homework exercise in finite elements, Inter. J. Num. Meth. in
Engineering 11 (1977) 411-418.
- Some recent contributions to plasticity theory, J. Franklin Institute
302 (1977) 429-442.
- 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.
- Uniqueness in the theory of variational inequalities, Advances
in Math. 22 (1976) 356-363.
- A minimax problem in plasticity theory, Functional Analysis Methods
in Numerical Analysis, ed. M.Z. Nashed, Springer Lecture Notes
701 (1979) 319-333.
- 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.
- 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).
- The solution of nonlinear finite element equations, with H. Matthies,
Inter. J. Num. Meth. in Eng. 14 (1979) 1613-1626.
- 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.
- 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.
- Existence de solutions relaxées pour les équations de
la plasticité, with R. Temam, Comptes Rendus Acad. Sc. Paris
287 (1978) 515-519.
- Functions of bounded deformation, with R. Temam, Arch. Rat.
Mech. Anal. 75 (1980) 7-21.
- 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).
- Duality and relaxation in the variational problems of plasticity, with
R. Temam, J. de Mécanique 19 (1980) 1-35.
- The quasi-Newton method in finite element calculations, Chapter 20
in Computational Methods in Nonlinear Mechanics, J.T. Oden, ed., North-Holland
(1980).
- 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.
- 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.
- Optimal design for torsional rigidity, with R. Kohn, Proc.
Int. Symp. on Mixed and Hybrid Finite Element Methods, Atlanta (1981).
- Optimal design of cylinders in shear, with R. Kohn, MAFELAP Conference,
Brunel (1981).
- The width of a chair, American Math. Monthly 89 (1982)
529-534.
- 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.
- 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.
- The optimal accuracy of difference schemes, with A. Iserles, Transactions
Amer. Math. Soc. 277 (1983) 770-803.
- Duality in the classroom, American Math. Monthly 91 (1984)
250-254.
- Maximal flow through a domain, Mathematical Programming 26
(1983) 123-143.
- Barriers to stability, with A. Iserles, SIAM J. Numerical Analysis
20 (1983) 1251-1257.
- 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.
- 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).
- A negative results for nonnegative matrices, Journal of Xian Jiaotong
University 17 (1983) 69-72.
- Numerical and biological shape optimization, with A. Philpott,
in ``Unification of Finite Element Methods,'' Math. Studies 94,
H. Kardestuncer, ed., North-Holland (1984).
- Explicit relaxation of a variational problem in optimal design, with
R. Kohn, Bull. Amer. Math. Soc. 9 (1983) 211-214.
- 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).
- The constrained least gradient problem, with R. Kohn, in Non-Classical
Continuum Mechanics, R. Knops and A. Lacey, eds., Cambridge
University Press (1987).
- The optimal design of a two-way conductor, with R. Kohn, in Nonsmooth
Mechanics, P.D. Panagiotopoulos et al, eds., Birkhäuser
(1987).
- 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).
- Optimal design in elasticity and plasticity, with R. Kohn, Int.
J. Numerical Meths. in Eng. 22 (1986) 183-188.
- A framework for equilibrium equations, SIAM Review 30
(1988) 283-297.
- Karmarkar's algorithm in a nutshell, SIAM News 18 (1985)
13.
- Karmarkar's algorithm and its place in applied mathematics, Math.
Intelligencer 9 (1987) 4-10.
- A proposal for Toeplitz matrix calculations, Studies in Appl. Math.
74 (1986) 171-176.
- The Toeplitz-circulant eigenvalue problem , with A. Edelman, pp. 109-117
in Oakland Conf. on PDE's and Applied Mathematics, L. Bragg and J. Dettman,
eds., Longman (1987).
- Patterns in linear algebra, American Math. Monthly 96
(1989) 105-117.
- Paradox lost: Natural boundary conditions in the Ritz- Galerkin method,
with J. Storch, Int. J. Numerical Methods in Engineering 26
(1988) 2255-2266.
- Dual extremum principles in finite elastoplastic deformation, with
Y. Gao, Acta Appl. Mathematicae 17 (1989) 257-268.
- Toeplitz equations by conjugate gradients with circulant preconditioner,
with R. Chan, SIAM J. Sci. Stat. Comp. 10 (1989) 104-119.
- Geometric nonlinearity: Potential energy, complementary energy, and
the gap function, with Y. Gao, Quarterly of Applied Mathematics
47 (1989) 487-504.
- Teaching modern engineering mathematics, Applied Mechanics Review
39 (1986) 1319-1321; SEFI Proceedings, L. Rade, ed., Chartwell-Bratt
(1988).
- Sums and differences vs. integrals and derivatives, College Mathematics
Journal 21 (1990) 20-27.
- Wavelets
and dilation equations: A brief introduction, SIAM Review 31
(1989) 614-627.
- Inverse problems and derivatives of determinants, Archive Rational
Mech. and Analysis 114 (1991) 255-265.
- A thousand points of light, with D. Hardin, Third Conference on
Technology in Collegiate Mathematics (1990).
- A chaotic search for i, College Math. Journal 22 (1991)
3-12.
- The optimal coefficients in Daubechies wavelets, Physica D
60 (1992) 239-244.
- Polar area is the average of strip areas, Amer. Math. Monthly
100 (1993) 250-254.
- The fundamental theorem of linear algebra, Amer. Math. Monthly
100 (1993) 848-855.
- Wavelet
transforms versus Fourier transforms, Bull. Amer. Math. Soc.
28 (1993) 288-305.
- Graphs, matrices, and subspaces, College Math. Journal 24
(1993) 20-28.
- The asymptotic probability of a tie for first place, with B. Eisenberg
and G. Stengle, Annals of Applied Probability 3 (1993)
731-745.
- 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.
- Convolution, reconstruction, and wavelets, Advances in Computational
Mathematics: New Delhi, H.P. Dikshit and C.A. Micchelli,
eds. (1994), World Scientific Publishing.
- Short wavelets
and matrix dilation equations, with V. Strela, IEEE Trans.
on Signal Processing 43 (1995) 108-115.
- Orthogonal
multiwavelets with vanishing moments, with V. Strela, Proc.
SPIE Conference on Mathematics of Imaging, J. Optical Eng. 33
(1994) 2104-2107.
- Wavelets,
American Scientist 82 (1994) 250-255.
- Every unit matrix is a LULU, Linear Algebra and Its Applications
265 (1997) 165-172.
- Finite
element multiwavelets, with V. Strela, Proc. Maratea NATO Conference,
Kluwer (1995).
- Approximation
by translates of refinable functions, with C. Heil and V. Strela,
Numerische Mathematik (1996).
- The cascade algorithm for the dilation equation, Proc. Argonne
Conference on Wavelets (1994).
- Eigenvalues and
convergence of the cascade algorithm, submitted to IEEE Trans. Signal
Processing 44 (1996).
- Multiwavelet filter banks for data compression, with P. Heller,
V. Strela, et al., IEEE Trans. Image Processing, to appear.
- Asymptotic analysis of Daubechies polynomials, with Jianhong Shen,
Proc. Amer. Math. Soc. 124 (1996) 3819-3833.
- Biorthogonal multiwavelets and finite elements, with V. Strela,
preprint (1996).
- Condition numbers for wavelets and filter banks, Computational and
Appl. Math. (Brasil) 15 (1996) 161-179.
- Asymptotic structures of Daubechies scaling functions and wavelets,
with Jianhong Shen, to appear in Appl. and Comp. Harmonic Analysis (1998).
- 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.
- Filter banks and wavelets, in Wavelets: Theory and Applications,
G. Erlebacher, M. Y. Hussaini, L. Jameson, eds., Oxford
Univ. Press (1996).
- Creating
and comparing wavelets, Numerical Analysis: A. R. Mitchell
Anniversary Volume, D. Griffiths, ed. (1996).
- Writing about mathematics, SIAM News , June (1996).
- The mathematics of GPS, SIAM News , June (1997).
- Wavelets, Iterative Methods in Scientific Computing, pp. 59-110,
R. Chan, T. Chan and G. Golub, eds., Springer (1997).
- The first moment
of wavelet random variables, with Y. Ma and B. Vidakovic,
preprint (1997).
- The search
for a good basis, Numerical Analysis 1997, D. Griffiths,
D. Higham, and A. Watson, eds., Addison Wesley Longman (1997).
- The
asymptotics
of optimal (equiripple) filters, with Jianhong Shen, IEEE
Trans. on Signal Processing 47 (1999) 1087-1098.
- Inhomogeneous
refinement equations, with Ding-Xuan Zhou, J. Fourier Analysis
and Applications 4 (1998) 733-747.
- Autocorrelation functions in GPS data processing: modeling aspects,
with Kai Borre, ION Conference (1997).
- A linear algebraic representation of the double entry accounting system,
with A. Arya, J. Fellingham, J. Glover, and D. Schroeder,
Manuscript (1998).
- The discrete cosine transform, block Toeplitz matrices, and filter
banks, Computational Mathematics, Shen, Micchelli, Xu, eds. Marcel Dekker
(1998).
- The discrete
cosine transform, SIAM Review 41 (1999) 135-147.
- The limits of
refinable functions, with Ding-Xuan Zhou, to appear in Trans. American
Math. Soc (2000).
- The
potential theory of several intervals and its applications, with
J. Shen and A. Wathen, to appear in Appl. Math. and Opt. (2000).
- Row reduction
of a matrix and A = CaB, with S. Lee, to appear in the American
Mathematical Monthly (2000).
- On wavelet fundamental solutions to the heat equation: Heatlets,
with J. Shen, J. Differential Eqns. 161 (2000)
403-421.
- 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. Contemorary
Mathematics 247 (1999) 285-296.
- Trees
with Cantor eigenvalue distribution, with Li He and Xiangwei
Liu, submitted to J. Combinatorial Theory (1999).
- Signal processing for everyone, to appear in Springer
Lecture Notes (2000).
- Eigenstructures of spatial design matrices, with D. Gorsich and
M. Genton, in preparation.
- On the factorization of M-channel paraunitary filter banks, with
X.Q. Gao and T. Nguyen, in preparation.
- 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.
- Laplacian
eigenvalues of growing trees, with Li He, and Xiangwei Liu,
to appear.
- Teaching and learning on the Internet, Math. Assoc. of
America, to appear (2001)
- Commentary on Paper #5, Collected Works of Gian-Carlo
Rota, to appear.
- Localized eigenvectors from widely spaced matrix modifications,
with Xiangwei Liu, Susan Ott, and Li He, in preparation.