Gilbert Strang

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Gilbert Strang is affiliated with the following schools: University of California, Los Angeles, Massachusetts Institute of Technology

Gilbert Strang's AcademicInfluence.com Rankings

Gilbert Strang

Mathematics

#70

World Rank

#200

Historical Rank

#25

USA Rank

Measure Theory

#189

World Rank

#295

Historical Rank

#83

USA Rank

mathematics Degrees

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Mathematics

Why Is Gilbert Strang Influential?

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According to Wikipedia, William Gilbert Strang is an American mathematician known for his contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing mathematics textbooks. Strang was the MathWorks Professor of Mathematics at the Massachusetts Institute of Technology. He taught Linear Algebra, Computational Science, and Engineering, Learning from Data, and his lectures are freely available through MIT OpenCourseWare.

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Gilbert Strang's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On the Construction and Comparison of Difference Schemes (1968) (3294)
Wavelets and filter banks (1996) (2976)
An Analysis of the Finite Element Method (1974) (2460)
Introduction to applied mathematics (1988) (1762)
A Simple Mesh Generator in MATLAB (2004) (1428)
Introduction to Linear Algebra (1993) (1352)
Wavelets and Dilation Equations: A Brief Introduction (1989) (1104)
Linear Algebra, Geodesy, and GPS (1997) (591)
The solution of nonlinear finite element equations (1979) (555)
Optimal design and relaxation of variational problems, III (1986) (519)
The application of multiwavelet filterbanks to image processing (1999) (456)
A proposal for toeplitz matrix calculations (1986) (426)
Computational Science and Engineering (2007) (402)
Wavelet transforms versus Fourier transforms (1993) (387)
The Discrete Cosine Transform (1999) (352)
Functions of bounded deformation (1980) (278)
VARIATIONAL CRIMES IN THE FINITE ELEMENT METHOD (1972) (262)
Accurate partial difference methods (1964) (261)
Short wavelets and matrix dilation equations (1995) (257)
Toeplitz equations by conjugate gradients with circulant preconditioner (1989) (241)
Topics in Nonsmooth Mechanics (1988) (193)
Mesh generation for implicit geometries (2005) (187)
Maximal flow through a domain (1983) (187)
Geometric nonlinearity: potential energy, complementary energy, and the gap function (1989) (186)
The Fundamental Theorem of Linear Algebra (1993) (180)
THE APPLICATION OF MULTIWAVELET FILTER BANKS TO IMAGE PROCESSING ∗ (1995) (175)
Approximation by translates of refinable functions (1996) (168)
A Fourier Analysis of the Finite Element Variational Method (2011) (167)
Orthogonal multiwavelets with vanishing moments (1994) (160)
Fourier Analysis of the Finite Element Method in Ritz-Galerkin Theory (1969) (142)
Approximation in the finite element method (1972) (141)
Accurate partial difference methods I: Linear cauchy problems (1963) (139)
On factorization of M-channel paraunitary filterbanks (2001) (116)
Piecewise polynomials and the finite element method (1973) (102)
The correctness of the Cauchy problem (1971) (88)
Optimal design in elasticity and plasticity (1986) (84)
Hencky-Prandtl nets and constrained Michell trusses (1983) (81)
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares [Bookshelf] (2020) (80)
The application of quasi‐Newton methods in fluid mechanics (1981) (78)
Trigonometric Polynomials and Difference Methods of Maximum Accuracy (1962) (77)
Eigenvalues of (↓2)H and convergence of the cascade algorithm (1996) (74)
THE OPTIMAL ACCURACY OF DIFFERENCE SCHEMES (1983) (74)
A Framework for Equilibrium Equations (1988) (71)
Operator splitting (2011) (63)
Smoothing by Savitzky-Golay and Legendre Filters (2003) (62)
One-sided approximation and variational inequalities (1974) (61)
Finite element multiwavelets (1994) (60)
The Asymptotic Probability of a Tie for First Place (1993) (55)
THE FINITE ELEMENT METHOD AND APPROXIMATION THEORY (1971) (55)
The Interplay of Ranks of Submatrices (2004) (52)
CONTINUITY OF THE JOINT SPECTRAL RADIUS: APPLICATION TO WAVELETS (1995) (47)
Functions of Difference Matrices Are Toeplitz Plus Hankel (2014) (44)
Algorithms for Global Positioning (2012) (44)
Asymptotics of Daubechies Filters, Scaling Functions, and Wavelets (1998) (43)
The dimension of piecewise polynomial spaces, and one-sided approximation (1974) (43)
Time-varying filter banks and multiwavelets (1994) (43)
Explicit relaxation of a variational problem in optimal design (1983) (42)
Karmarkar’s algorithm and its place in applied mathematics (1987) (41)
L1 and L∞ Approximation of Vector Fields in the Plane (1983) (39)
A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level (2021) (39)
Necessary and insufficient conditions for well-posed Cauchy problems (1966) (38)
A study of two-channel complex-valued filterbanks and wavelets with orthogonality and symmetry properties (2002) (38)
Inhomogeneous refinement equations (1998) (37)
Balanced Splitting and Rebalanced Splitting (2013) (35)
Inferring Transactions from Financial Statements (2000) (34)
On the Kantorovich inequality (1960) (34)
Maximum flows and minimum cuts in the plane (2010) (32)
Multiwavelet filter banks for data compression (1995) (31)
Dual extremum principles in finite deformation elastoplastic analysis (1989) (31)
A minimax problem in plasticity theory (1979) (30)
Gaussian mixture models of ECoG signal features for improved detection of epileptic seizures. (2004) (29)
Asymptotic analysis of Daubechies polynomials (1996) (28)
On Strong Hyperbolicity (1967) (28)
Fast transforms: Banded matrices with banded inverses (2010) (28)
Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties (2001) (27)
Structural design optimization, homogenization and relaxation of variational problems (1982) (26)
Numerische lineare Algebra (2003) (26)
The optimal coefficients in Daubechies wavelets (1992) (24)
Matrices with prescribed Ritz values (2008) (24)
Trees with Cantor Eigenvalue Distribution (2003) (24)
Polynomial approximation of Bernstein type (1962) (24)
The Potential Theory of Several Intervals and Its Applications (2001) (23)
Computational mathematics driven by industrial problems (2000) (23)
Approximating semigroups and the consistency of difference schemes (1969) (23)
Optimal design for torsional rigidity (1982) (22)
Optimal Conditioning of Matrices (1973) (21)
Every unit matrix is a LULU (1997) (21)
The Width of a Chair (1982) (21)
A Chaotic Search for i (1991) (20)
Random Triangle Theory with Geometry and Applications (2015) (20)
Optimal stability for trapezoidal–backward difference split-steps (2010) (19)
Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic (2017) (19)
The Laplacian eigenvalues of a polygon (2004) (18)
The asymptotics of optimal (equiripple) filters (1999) (18)
Mathematical and Computational Methods in Plasticity (1980) (17)
On Wavelet Fundamental Solutions to the Heat Equation—Heatlets (2000) (17)
Matrix theorems for partial differential and difference equations (1965) (16)
The Green’s function for the Hückel (tight binding) model (2014) (15)
Toeplitz operators in a quarter-plane (1970) (15)
Eigenstructures of Spatial Design Matrices (2002) (15)
Non-Classical Continuum Mechanics: The Constrained Least Gradient Problem (1987) (15)
Hyperbolic initial-boundary value problems in two unknowns (1969) (14)
A family of model problems in plasticity (1979) (14)
Laplace eigenvalues on regular polygons: A series in 1/N (2012) (14)
Inverse problems and derivatives of determinants (1991) (14)
Green’s matrices (2010) (14)
Groups of banded matrices with banded inverses (2011) (13)
Paradox lost: Natural boundary conditions in the Ritz–Galerkin method (1988) (13)
Compactly Supported Refinable Functions with Infinite Masks (1999) (13)
Differential Equations and Linear Algebra (2014) (13)
The Jordan forms of AB and BA (2009) (12)
Signal processing for everyone (2000) (12)
Implicit difference methods for initial-boundary value problems☆ (1966) (12)
A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More (2021) (12)
The limits of refinable functions (2001) (11)
Binomial Matrices (2001) (11)
Maximum area with Minkowski measures of perimeter (2008) (11)
Localized Eigenvectors from Widely Spaced Matrix Modifications (2003) (11)
Student Solutions Manual for Strang's Linear Algebra and Its Applications (2005) (10)
Wavelets from filter banks (1996) (10)
Creating and comparing wavelets (1996) (10)
Circuit simulation and moving mesh generation (2004) (10)
Spectral decomposition in advection-diffusion analysis by finite element methods (1978) (10)
The asymptotic Toeplitz-circulant eigenvalue problem (1987) (9)
Barriers to Stability (1983) (9)
On multiple characteristics and the levi-lax conditions for hyperbolicity (1969) (9)
Essays in Linear Algebra (2012) (9)
A Thousand Points of Light (1990) (8)
Sums and Differences vs. Integrals and Derivatives. (1990) (8)
Introduction to applied mathematics / Gilbert Strang (1986) (8)
Nonlinear partial differential equations in applied science : proceedings of the U.S.-Japan seminar, Tokyo, 1982 (1983) (8)
The Finite Element Method--Linear and Nonlinear Applications (1974) (8)
Patterns in linear algebra (1989) (7)
Duality in the Classroom (1984) (7)
Polar area is the average of strip areas (1993) (7)
The Joint Spectral Radius (2003) (7)
One-sided approximation and plate bending (1973) (6)
Permutations as Product of Parallel Transpositions (2011) (6)
Calculus Volume 2 (2016) (6)
Optimal design of a two-way conductor (1988) (6)
Row Reduction of a Matrix and A = CaB (2000) (5)
Eigenvalues of Toeplitz matrices with 1 × 2 blocks (1996) (5)
Banded Matrices with Banded Inverses and A = LPU (2011) (5)
Calculus Volume 1 (2016) (5)
Unbalanced Polynomials and Difference Methods for Mixed Problems (1965) (5)
Optimal design of cylinders in shear (1982) (5)
Free boundaries and finite elements in one dimension (1975) (5)
ERRATA TO: APPROXIMATION BY TRANSLATES OF REFINABLE FUNCTIONS (1997) (5)
The Algebra of Elimination (2015) (4)
Three Matrix Factorizations from the Steps of Elimination (2022) (4)
Advances in applied mathematics and global optimization : in honor of Gilbert Strang (2009) (4)
Pseudo-biorthogonal Multiwavelets and Finite Elements (1997) (4)
The main diagonal of a permutation matrix (2011) (4)
Application of Multiwavelets to Signal Compression and Denoising (1995) (3)
Arc Length and Curvature (2016) (3)
A problem in capillarity and plasticity (1982) (3)
A homework exercise in finite elements (1977) (3)
Laplacian Eigenvalues of Growing Trees (2000) (3)
Moments and Centers of Mass (2016) (3)
Doceamus: The Core Ideas in Our Teaching (2014) (3)
18.085 Computational Science and Engineering I, Fall 2007 (2007) (3)
Multiplying and Factoring Matrices (2018) (3)
On two-channel orthogonal and symmetric complex-valued FIR filter banks and their corresponding wavelets (2002) (2)
Parametric Equations and Polar Coordinates (2016) (2)
The Nucleus of a Set (1968) (2)
A Local Inverse Formula and a Factorization (2016) (2)
Autocorrelation Functions in GPS Data Processing: Modeling Aspects (1997) (2)
Calculus Volume 3 (2016) (2)
LU and CR Elimination (2022) (2)
APPENDIX C – RETRACTED: COMPUTER CODES FOR LINEAR ALGEBRA (1980) (2)
Linear Algebra@@@Linear Algebra and its Applications@@@Linear Algebra: A Geometric Approach@@@Introduction to Linear Algebra (2005) (2)
Chapter 14 Numerical & Biological Shape Optimization (1984) (2)
6 – RETRACTED: POSITIVE DEFINITE MATRICES (1980) (2)
Some recent contributions to plasticity theory (1976) (2)
Learning from 100 Numbers (2005) (2)
Graphs, Matrices, and Subspaces (1993) (2)
3 – RETRACTED: ORTHOGONAL PROJECTIONS AND LEAST SQUARES (1980) (1)
8 – RETRACTED: LINEAR PROGRAMMING AND GAME THEORY (1980) (1)
WITHDRAWN: COMPUTER CODES FOR LINEAR ALGEBRA (1980) (1)
Symmetric elimination without pivoting (2014) (1)
On numerical ranges and holomorphic semigroups (1969) (1)
Taylor and Maclaurin Series (2016) (1)
RETRACTED: Front Matter (1980) (1)
Calculus: Volume 3 (OpenStax) (2016) (1)
Double Integrals over General Regions (2016) (1)
4.9 Newton’s Method (2016) (1)
Fibered structures in optimal design (1986) (1)
BLOCK TRIDIAGONAL MATRICES AND THE KALMAN FILTER (2002) (1)
Notes on Softening and Local Instability (1983) (1)
18.06 Linear Algebra, Spring 2005 (2005) (1)
LINEAR ALGEBRA and Learning from Data First Edition MANUAL FOR INSTRUCTORS (2019) (1)
1 – WITHDRAWN: GAUSSIAN ELIMINATION (1980) (1)
Stability analysis of a chain of non-identical vehicles under bilateral cruise control (2019) (1)
5.2 The Definite Integral (2016) (0)
Double Integrals in Polar Coordinates (2016) (0)
Conservative Vector Fields (2016) (0)
The Cross Product (2016) (0)
1.2 Basic Classes of Functions (2016) (0)
The Logistic Equation (2016) (0)
Proceedings of the 10th International Technical Meeting of the Satellite Division of the Institute of Navigation GPS-97, September 16-19, 1997 (1997) (0)
Basics of Differential Equations (2016) (0)
WITHDRAWN: THE JORDAN FORM (1980) (0)
Linear Algebra Online and Offline: The 2015 Lin Lectures (2015) (0)
Autocorrelation Functionsin GPS DataProcessing: Modeling Aspects (1997) (0)
6.2 Determining Volumes by Slicing (2016) (0)
Power Series and Functions (2016) (0)
5.1 Approximating Areas (2016) (0)
3.9 Derivatives of Exponential and Logarithmic Functions (2016) (0)
3.3 Differentiation Rules (2016) (0)
Series Solutions of Differential Equations (2016) (0)
4.5 Derivatives and the Shape of a Graph (2016) (0)
RETRACTED: SOLUTIONS TO EXERCISES (1980) (0)
6.5 Physical Applications (2016) (0)
Areas between Curves (2016) (0)
Vectors in Three Dimensions (2016) (0)
18.085 Mathematical Methods for Engineers I, Fall 2005 (2002) (0)
Error bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions (2022) (0)
First-order Linear Equations (2016) (0)
Elimination and Factorization (2023) (0)
The Fundamental Theorem of Calculus (2016) (0)
The Divergence Theorem (2016) (0)
The Changing Face of Applied Mathematics (2010) (0)
Properties of Power Series (2016) (0)
Area and Arc Length in Polar Coordinates (2016) (0)
6.9 Calculus of the Hyperbolic Functions (2016) (0)
Gilbert Strang Kieval lecture, April 1994 (1994) (0)
Edinburgh Explorer Higher Order Derivative Estimates for Finite-difference Schemes for Linear Elliptic and Parabolic Equations (2018) (0)
LINEAR ALGEBRA FOR EVERYONE (2020) (0)
Die Mathematik hinter der Satellitennavigation (1997) (0)
Second-Order Linear Equations (2016) (0)
2.4 Continuity (2016) (0)
6.8 Exponential Growth and Decay (2016) (0)
Calcukus Volume 2 (2007) (0)
3.6 The Chain Rule (2016) (0)
3.1 Defining the Derivative (2016) (0)
5 – RETRACTED: EIGENVALUES AND EIGENVECTORS (1980) (0)
2.3 The Limit Laws (2016) (0)
Exponential Growth and Decay (2016) (0)
Research and Tutorial Exposition (2002) (0)
Divergence and Curl (2016) (0)
6.6 Moments and Centers of Mass (2016) (0)
3.2 The Derivative as a Function (2016) (0)
18.086 Mathematical Methods for Engineers II, Spring 2005 (2005) (0)
Lecture 33: Filters, Fourier Integral Transform and Lecture 34: Fourier Integral Transform (Part 2) (2008) (0)
Uniqueness in the theory of variational inequalities (1976) (0)
Triple Integrals in Cylindrical and Spherical Coordinates (2016) (0)
3.8 Implicit Differentiation (2016) (0)
18.06 Linear Algebra, Fall 2002 (2002) (0)
Directional Derivatives and the Gradient (2016) (0)
Cylindrical and Spherical Coordinates (2016) (0)
Calculus of Parametric Curves (2016) (0)
Vectors in the Plane (2016) (0)
Applied Mathematics is Worldwide( 10 th Anniversary) (2000) (0)
Determining Volumes by Slicing (2016) (0)
APPENDIX A – RETRACTED: LINEAR TRANSFORMATIONS, MATRICES, AND CHANGE OF BASIS (1980) (0)
Vector-Valued Functions (2019) (0)
Nonhomogeneous Linear Equations (2016) (0)
Other Strategies for Integration (2016) (0)
5.6 Integrals Involving Exponential and Logarithmic Functions (2016) (0)
Double Integrals over Rectangular Regions (2016) (0)
Chapter 4 Review Exercises (2016) (0)
5.4 Integration Formulas and the Net Change Theorem (2016) (0)
Convolution (part 2), Filtering (2008) (0)
The Teaching of Engineering Mathematics (1986) (0)
The Divergence and Integral Tests (2016) (0)
Working with Taylor Series (2016) (0)
QnAs with Gilbert Strang. Interviewed by Farooq Ahmed. (2011) (0)
Balanced Splitting and Rebalanced Splitting Citation (2013) (0)
DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA MANUAL FOR INSTRUCTORS (2015) (0)
Teaching Applied Mathematics (2017) (0)
Chapter 1 Review Exercises (2016) (0)
Three steps on an open road (2013) (0)
Data Smoothing: Research 2002 (2003) (0)
LINEAR ALGEBRA: A HAPPY CHANCE TO APPLY MATHEMATICS (2008) (0)
3.5 Derivatives of Trigonometric Functions (2016) (0)
6.3 Volumes of Revolution: Cylindrical Shells (2016) (0)
Integration by Parts (2016) (0)
4.8 L’Hôpital’s Rule (2016) (0)
2.2 The Limit of a Function (2016) (0)
Review of Pre-Calculus (2016) (0)
1.4 Inverse Functions (2016) (0)
5.7 Integrals Resulting in Inverse Trigonometric Functions (2016) (0)
Starting with Two Matrices (2009) (0)
1.3 Trigonometric Functions (2016) (0)
A variant of Carathéodory's problem (1968) (0)
The Victory of Orthogonality (2020) (0)
4.6 Limits at Infinity and Asymptotes (2016) (0)
APPENDIX B – RETRACTED: THE JORDAN FORM (1980) (0)
Lecture 33: Left and right inverses; pseudoinverse (1999) (0)
Chapter 3 Review Exercises (2016) (0)
4.7 Applied Optimization Problems (2016) (0)
Equations of Lines and Planes in Space (2016) (0)
Ratio and Root Tests (2016) (0)
Calculus Volume 1: OpenStax (2016) (0)
4 – RETRACTED: DETERMINANTS (1980) (0)
Functions with Infinite Masks (2007) (0)
Green’s Theorem (2016) (0)
An elementary proof of Mirsky's low rank approximation theorem (2020) (0)
CHAPTER V – THE DEFINITE INTEGRAL (1965) (0)
Vector-Valued Functions and Space Curves (2016) (0)
Optimal Design of Fibered Structures. (1988) (0)
QR Decomposition An Annotated Bibliography (2009) (0)
The Dot Product (2016) (0)
The Pseudoinverse of A=CR is A+=R+C+ (?) (2023) (0)
1.5 Exponential and Logarithmic Functions (2016) (0)
Motion in Space (2016) (0)
7 – RETRACTED: COMPUTATIONS WITH MATRICES (1980) (0)
3.7 Derivatives of Inverse Functions (2016) (0)
Calculus of Vector-Valued Functions (2016) (0)
Chapter 5 Review Exercises (2016) (0)
4.4 The Mean Value Theorem (2016) (0)
Lecture 29: Singular value decomposition (1999) (0)
The teaching of calculus : careful changes (1992) (0)
Table of Integrals (2016) (0)
2.1 A Preview of Calculus (2016) (0)
6.7 Integrals, Exponential Functions, and Logarithms (2016) (0)
Lecture Notes: Handouts 1–16 (2013) (0)
Chapter 2 Review Exercises (2016) (0)
Table of Derivatives (2016) (0)
Calculus Volume 2: OpenStax (2016) (0)
2 – WITHDRAWN: THE THEORY OF SIMULTANEOUS LINEAR EQUATIONS (1980) (0)
Direction Fields and Numerical Methods (2016) (0)
Tangent Planes and Linear Approximations (2016) (0)
Calculating Centers of Mass and Moments of Inertia (2016) (0)
Optimal Shape Design for Elliptic Systems (Olivier Pironneau) (1986) (0)
6.4 Arc Length of a Curve and Surface Area (2016) (0)
2.5 The Precise Definition of a Limit (2016) (0)
4.2 Linear Approximations and Differentials (2016) (0)
Starting with the right matrices (2007) (0)
5.5 Substitution (2016) (0)
5.3 The Fundamental Theorem of Calculus (2016) (0)
1.1 Review of Functions (2016) (0)
Change of Variables in Multiple Integrals (2016) (0)
6.1 Areas between Curves (2016) (0)
4.1 Related Rates (2016) (0)
Functions of Several Variables (2020) (0)
NICE FUNCTIONS (2014) (0)
Maxima/Minima Problems (2016) (0)
4.3 Maxima and Minima (2016) (0)
3.4 Derivatives as Rates of Change (2016) (0)
Differentiation of Functions of Several Variables (2016) (0)

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What Schools Are Affiliated With Gilbert Strang?

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