Gilbert Strang

GILBERT STRANG

Work:
Room 2—240, M.I.T.
Cambridge MA 02139

Phone: [phone]
Fax: [phone]
e-mail: ude.tim.htam|sg#ude.tim.htam|sg
URL:
http://math.mit.edu/~gs

EDUCATION

1. 1952-1955 William Barton Rogers Scholar, M.I.T. (S.B. 1955)
2. 1955-1957 Rhodes Scholar, Oxford University (B.A., M.A. 1957)
3. 1957-1959 NSF Fellow, UCLA (Ph.D. 1959)

POSITIONS HELD

1. 1959-1961 C.L.E. Moore Instructor, M.I.T.
2. 1961-1962 NATO Postdoctoral Fellow, Oxford University
3. 1962-1964 Assistant Professor of Mathematics, M.I.T.
4. 1964-1970 Associate Professor of Mathematics, M.I.T.
5. 1970- Professor of Mathematics, M.I.T.

AWARDS AND DUTIES
1 Alfred P. Sloan Fellow (1966—1967)
2 Chairman, M.I.T. Committee on Pure Mathematics (1975-1979)
3 Chauvenet Prize, Mathematical Association of America (1976)
4 Council, Society for Industrial and Applied Mathematics (1977-1982)
5 NSF Advisory Panel on Mathematics (1977-1980) (Chairman 1979-1980)
6 CUPM Subcommittee on Calculus (1979-1981)
7 Fairchild Scholar, California Institute of Technology (1980-1981)
8 Honorary Professor, Xian Jiaotong University, China (1980)
9 American Academy of Arts and Sciences (1985)
10.Taft Lecturer, University of Cincinnati (1977)
11.Gergen Lecturer, Duke University (1983)
12.Lonseth Lecturer, Oregon State University (1987)
13.Magnus Lecturer, Colorado State University (2000)
14.Blumberg Lecturer, University of Texas (2001)
15.AMS-SIAM Committee on Applied Mathematics (1990-1992)
16.Vice President for Education, SIAM (1991-1996)
17.MAA Science Policy Committee (1992-1995)
18.Committee on the Undergraduate Program in Mathematics, MAA (1993-1996)
19.President of SIAM (1999-2000)
20.Chair, Joint Policy Board for Mathematics (1999)
21.Chair, SIAM Committee on Science Policy (2001-2002)
22.Honorary Fellow, Balliol College, Oxford (1999)
23.Honorary Member, Irish Mathematical Society (2002)
24.US National Committee on Mathematics (2001-2004, Chair 2003-2004)
25.Award for Distinguished Service to the Profession, SIAM (2003)
26.Graduate School Teaching Award, MIT (2003)
27.Abel Prize Committe, Oslo (2003-2005)
28.Von Neumann Prize Medal, US Association for Computational Mechanics (2005)
29.Ford Prize for "Pascal Matrices" with Alan Edelman, Mathematical Association
of America (2005)
30.Distinguished University Teacher of Mathematics, New England Section,
Mathematical Association of America (2006)
31.Franklin and Deborah Tepper Haimo Prize, MAA (2006)
32.Su Buchin Prize, International Congress of Industrial and Applied Mathematics
(ICIAM, Zurich, 2007)
33.Henrici Prize (ICIAM, Zurich, 2007)
34.National Academy of Sciences (2009)
35.Doctor Honoris Causa, University of Toulouse (2010)

JOURNAL EDITOR
1 Numerische Mathematik (Honorary Editor from 1996)
2 International Journal for Numerical Methods in Engineering
3 Archive for Rational Mechanics and Analysis (to 1990)
4 Studies in Applied Mathematics
5 Computer Methods in Applied Mechanics and Engineering (to 2004)
6 SIAM Journal of Numerical Analysis (to 1977)
7 Numerical Functional Analysis and Optimization
8 Physica D: Nonlinear Phenomena (to 1986)
9 Communications in Numerical Methods in Engineering
10.SIAM Journal on Matrix Analysis and Applications (to 1993)
11.Acta Applicandae Mathematicae
12.Proceedings of the Edinburgh Mathematical Society (to 1993)
13.Mathematical Modelling and Numerical Analysis
14.Japan Journal of Applied Mathematics
15.Structural Optimization
16.Royal Society of Edinburgh, Proceedings A
17.Computational Optimization and Applications
18.SIAM Review (to 2001)
19.COSMOS, National University of Singapore
20.Numerical Algorithms (to 2004)
21.Communications in Information and Systems
22.International Journal of Mathematics and Computer Science
23.Communications in Information and Systems
24.International Journal of Mathematics and Computer Science

BOOKS (with Russian, Japanese and Chinese translatins if the frst twi):
1 An Analysis of the Finite Element Method, with George Fix, Prentice-Hall
(1973). Second Edition, Wellesley-Cambridge Press (2008).
2 Linear Algebra and Its Applications, Academic Press (1976). Second edition:
Harcourt Brace Jovanovich (1980). Third edition: Brooks/Cole (1988). Fourth
edition: Brooks/Cole (2006).
3 Introduction to Applied Mathematics, Wellesley-Cambridge Press (1986).
4 Nonlinear Partial Differential Equations in Applied Science, H. Fujita, P. Lax, G.
Strang, editors, Lecture Notes in Numerical and Applied Analysis 5,
Kinokuniya/North Holland (1982).
5 Topics in Nonsmooth Mechanics, J.J. Moreau, P.D. Panagiotopoulos, G. Strang,
editors, Birkhauser (1988).
6 Calculus, Wellesley-Cambridge Press (1991). Second Edition (2010).
7 Introduction to Linear Algebra, Wellesley-Cambridge Press (1993). Second
Edition (1998). Third Edition (2003). Fourth Edition (2009)
8 Wavelets and Filter Banks, with Truong Nguyen, Wellesley-Cambridge Press
(1996).
9 Linear Algebra, Geodesy, and GPS, with Kai Borre, Wellesley-Cambridge Press
(1997).
10.Computational Science and Engineering, Wellesley-Cambridge Press (2007).
11.Algorithms for Global Positioning, with Kai Borre, Wellesley-Cambridge Press
(2011).
12.Essays in Linear Algebra, Wellesley-Cambridge Press (2012).
13.Differential Equations and Linear Algebra, Wellesley-Cambridge Press (2014).

VIDEO LECTURES (on MIT OpenCourseWAre) ocw.mit.edu

18.06 Linear Algebra

18.085-086 Computational Science and Engineering

Highlights of Calculus

Differential Equations - 50 new videos on ocw.mit.edu and on Mathworks.com

BYU - Life of a Mathematician, Calculus vs. Linear Algebra, Random Triangle:
Acute or Obtuse?

BIBLIOGRAPHY
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, C. Micchelli, J. 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 (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, Studies in Applied Mathematics 110 (2003) 123-136.
136
Eigenstructures of spatial design matrices, with D. Gorsich and M.
Genton, J. Multivariate Analysis 80 (2002) 138-165.
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,Medical Eng. and Physics (2004).
139
Laplacian eigenvalues of growing tees , 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, (2001)
141
The joint spectral radius , Commentary on paper # 5 , Collected Works of
Gian-Carlo Rota (2001).
142
Localized eigenvectors from widely spaced matrix modifications, with
Xiangwei Liu and Susan Ott, SIAM J. Discrete Math 16 (2003) 479-498.
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
Block tridiagonal matrices and the Kalman filter, Wavelet Analysis: Twenty
Years Developments, D.X. Zhou, ed., World Scientific Press (2002).
148
Smoothing by Savitzky-Golay and Legendre filters, with Per-Olof Persson,
in Mathematical Systems Theory , IMA Vol. 134, J. Rosenthal and D. Gilliam,
eds., Springer (2002).
149
Too Much Calculus, SIAM Linear Algebra Activity Group
Newsletter (2002); web.mit.edu/18.06.
150
Pascal matrices, with Alan Edelman, American Math. Monthly, 111 (2004)
189-197.
151
The Laplacian eigenvalues of a polygon , with Pavel Grinfeld, Computers
and Mathematics with Applications 48 (2004) 1121-1133.
152
A simple mesh generator in MATLAB, with Per-Olof Persson, SIAM
Review, 46 (2004). 329-345.
153
The interplay of ranks of submatrices , with Tri Nguyen, SIAM
Review 46 (2004) 637-646.
154
Circuit simulation and moving mesh generation, with Per-Olof
Persson, Proceedings Int. Symp. Comm. & Inf. Technology (ISCIT), Sapporo
(2004).
155
Linear algebra: A happy chance to apply mathematics, Proc. Int. Congress
on Math. Education (ICME-10), Denmark (2004).
156
Book review: The SIAM 100-digit Challenge, Science 307 (2005) 521-522.
157
Peter Lax Wins Abel Prize, SIAM News 38 (2005).
158
A Remarkable Eye for Out-of-the-Ordinary Mathematics (interview with L.
Mahadevan), SIAM News 38 (2005).
159
Matrices with prescribed Ritz values, with B. Parlett, Linear Algebra and
Its Applications 428 (2008). 1725-1739.
160
Maximum flows and minimum cuts in the plane , Journal of Global
Optimization, (2008); also in Advances in Mechanics and Mathematics, Volume
III, D. Gao and H. Sgerlai, eds. (2008).
161
Maximum area with Minkowski measures of perimeter , Proc. Royal Soc.
Edinburgh 138A (2008) 189-199.
162
Starting With Two Matrices , (2008), Mathematics Magazine 82 (2009).
278-283.
163
Optimal stability for trapezoidal-backward difference split-steps , with S.
Dharmaraja and Y. Wang, IMA J. Numerical Analysis 30 (2010) 141-148.
164
The Four Fundamental Subspaces: 4 Lines
165
QR Decomposition: An Annotated Bibliography, with M.L.R. de Campos,
Chapter 1 in QRD-RLS Adaptive Filtering, J. Apolinario, ed., Springer (2009).
166
The Jordan forms of AB and BA, with Ross Lippert, Electronic Journal of
Linear Algebra 18 (2009) 281-288.
167
Laplace eigenvalues on regular polygons: A series in 1/N, with Pavel
Grinfeld, J. Math. Analysis and Applications 385 (2012) 135-148.
168
Green's matrices, with V. Olshevsky and P. Zhlobich, Linear Algebra and
Its Applications, 432 (2010) 218-241.
169
Random triangle theory with geometry and applications, with Alan
Edelman, Foundations of Computational Mathematics, submitted.
170
Proofs of the Spectral Theorem, with Alan Edelman, web.mit.edu/18.06
171
"The Calculus of Friendship", book review, SIAM News 12/09.
172
Fast transforms: Banded matrices with banded inverses , Proc. National
Academy of Sciences 107 (#28) (2010) 12413-12416.
173
Introducing ex, in A Century of Advancing Mathematics, MAA Centennial
Volume, P. Zorn et al, eds. (2015).
174
Groups of banded matrices with banded inverses , Proc. Amer. Math Soc.
139 (2011) 4255-4264.
175
Permutations as products of parallel transpositions, with Chase Albert, Chi-
Kwong Li and Gexin Yu, SIAM Journal of Discrete Mathematics 25 (2011) 1412-
1417
176
Banded matrices with banded inverses and A = LPU , Proc. Fifth Intl.
Congress of Chinese Mathematicians : ICCM2010, International Press and Amer.
Math. Soc. (2012).
177
Triangular factorizations: The algebra of elimination , in Excursions in
Harmonic Analysis vol. 3, J. J. Benedetto et al., eds, Springer (2014).
178
Balanced splitting and rebalanced splitting, with R. L. Speth, W. H. Green,
and S. MacNamara, SIAM J. Numerical Analysis 56 (2013) 3084-3105.
179
The main diagonal of a permutation matrix, with M. Lindner, Linear
Algebra and Its Applications 439 (2013) 524-537.
180
Symmetric elimination without pivoting, with P. Van Dooren, Linear
Algebra and Its Applications 452 (2014) 40-45.
181
Functions of difference matrices are Toeplitz plus Hankel, with S.
MacNamara, SIAM Review 56 (2014) 525-546.
182
Three steps on an open road, Inverse Problems and Imaging 7 (2013) 961-
966
183
Operator splitting, with S. MacNamara, in Operator Splitting and
Alternating Direction Methods, R. Glowinski, S. Osher and W. Yin, eds., to
appear.
184
Master equations, with S. MacNamara, to be submitted to SIAM News.
185
The core ideas in our teaching, Notices of the American Mathematical
Society (2014), to appear.
186
Row rank equals column rank, to appear in Image (International Linear
Algebra Society newsletter).
187
Nice functions, manuscript.