**GILBERT STRANG**

**Work:**

Room 2—240, M.I.T.

Cambridge MA 02139

**Phone:** 617-253-4383

**Fax:** 617-253-4358

**e-mail:** ude.tim.htam|sg#ude.tim.htam|sg

**URL:**

http://math.mit.edu/~gs

**EDUCATION**

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

**POSITIONS HELD**

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

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26.Fourier analysis of the finite element method in Ritz-Galerkin theory, with

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27.Toeplitz operators in a quarter-plane, Bull. Amer. Math. Soc. 76 (1970) 1303-

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28.The correctness of the Cauchy problem, with H. Flaschka, Advances in

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29.The finite element method and approximation theory, SYNSPADE Proceedings,

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30.The change in solution due to change in domain, with A. Berger, AMS

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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-

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34.A Fourier analysis of the finite element variational method, with

G. Fix, Constructive Aspects of Functional Analysis, Edizioni Cremonese, Rome

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35.Piecewise polynomials and the finite element method, AMS Bulletin 79 (1973)

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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

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38.One-sided approximation and plate bending, Lecture Notes in Computer

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39.One-sided approximation and variational inequalities, with U. Mosco, Bull. Amer.

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40.The finite element method—linear and nonlinear applications, Proc. Intern.

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41.Free boundaries and finite elements in one dimension, with W. Hager, Math.

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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.