C. William Gear

Q: What Schools Are Affiliated With C. William Gear

C. William Gear is affiliated with the following schools: Princeton University, University of Illinois Urbana-Champaign, University of Cambridge

C. William Gear's AcademicInfluence.com Rankings

C. William Gear

Mathematics

#1549

World Rank

#2521

Historical Rank

#629

USA Rank

Measure Theory

#584

World Rank

#814

Historical Rank

#240

USA Rank

mathematics Degrees

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Mathematics

Why Is C. William Gear Influential?

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According to Wikipedia, C. William Gear was a British-American mathematician who specialized in numerical analysis and computer science. Gear was an American citizen. Gear studied at the University of Cambridge with a bachelor's degree in 1957 and an M.A. in 1960, and at the University of Illinois, Urbana-Champaign with an M.S. in 1957 and a Ph.D. in 1960 under Abraham H. Taub with his thesis Singular Shock Intersections in Plane Flow. From 1960 to 1962, he worked as an engineer for IBM. From 1962 to 1990, he was a professor of computer science at the University of Illinois, Urbana-Champaign, where he was the head of the computer science department from 1985 to 1990. From 1992 to 2000, he was president of the NEC Research Institute in Princeton.

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C. William Gear'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

Numerical initial value problem~ in ordinary differential eqttations (1971) (3234)
Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis (2003) (745)
The automatic integration of ordinary differential equations (1971) (645)
Simultaneous Numerical Solution of Differential-Algebraic Equations (1971) (632)
ODE METHODS FOR THE SOLUTION OF DIFFERENTIAL/ALGEBRAIC SYSTEMS (1984) (477)
Automatic integration of Euler-Lagrange equations with constraints (1985) (445)
Equation-free: The computer-aided analysis of complex multiscale systems (2004) (382)
A User’s View of Solving Stiff Ordinary Differential Equations (1979) (309)
Multirate linear multistep methods (1984) (307)
Differential-algebraic equations index transformations (1988) (279)
Algorithm 407: DIFSUB for solution of ordinary differential equations [D2] (1971) (278)
The automatic integration of stiff ordinary differential equations (1968) (263)
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum (2002) (261)
The index of general nonlinear DAEs (1995) (260)
s-step iterative methods for symmetric linear systems (1989) (226)
'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods (2002) (215)
Numerical Methods for Ordinary Differential Equations (1989) (206)
Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes (2004) (177)
Multibody Grouping from Motion Images (1998) (164)
The numerical integration of ordinary differential equations (1967) (148)
Differential algebraic equations, indices, and integral algebraic equations (1990) (145)
Hybrid Methods for Initial Value Problems in Ordinary Differential Equations (1965) (140)
Numerical integration of ordinary differential equations of various orders (1966) (135)
Iterative Solution of Linear Equations in ODE Codes (1983) (132)
The gap-tooth method in particle simulations (2003) (117)
Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks (2002) (116)
Solving Ordinary Differential Equations with Discontinuities (1984) (105)
An American National Standard- IEEE Standard for Binary Floating-Point Arithmetic (1985) (102)
Approximation methods for the consistent initialization of differential-algebraic equations (1988) (99)
Intrinsic map dynamics exploration for uncharted effective free-energy landscapes (2016) (97)
Differential-Algebraic Equations (1984) (93)
Maintianing solution invariants in the numerical solution of ODEs (1986) (90)
Deciding the Nature of the Coarse Equation through Microscopic Simulations: The Baby-Bathwater Scheme (2002) (82)
Parallel methods for ordinary differential equations (1988) (78)
Coarse projective kMC integration: forward/reverse initial and boundary value problems (2003) (77)
Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation (2003) (74)
Telescopic projective methods for parabolic differential equations (2003) (69)
Differential/algebraic systems and matrix pencils (1983) (68)
Stability and convergence of variable order multistep methods (1974) (62)
On the efficient implementation of preconditioned s-step conjugate gradient methods on multiprocessors with memory hierarchy (1989) (61)
DIFSUB for Solution of Ordinary Differential Equations [D2] (Algorithm 407) (1971) (54)
Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models (2003) (54)
Analysis of the accuracy and convergence of equation-free projection to a slow manifold (2007) (53)
Reduced models in chemical kinetics via nonlinear data-mining (2013) (50)
Runge-Kutta Starters for Multistep Methods (1978) (50)
Computing the structural index (1986) (49)
Second-order accurate projective integrators for multiscale problems (2005) (47)
Application of Coarse Integration to Bacterial Chemotaxis (2003) (47)
NUMERICAL INTEGRATION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS. Report No. 221. (1967) (47)
Numerical Solution of Ordinary Differential Equations: Is There Anything Left to Do? (1981) (47)
Raster-scan hidden surface algorithm techniques (1977) (46)
Data-Driven Reduction for a Class of Multiscale Fast-Slow Stochastic Dynamical Systems (2016) (40)
Does variable step size ruin a symplectic integrator (1992) (39)
From molecular dynamics to coarse self-similar solutions: a simple example using equation-free computation (2003) (38)
Computer Organization and Programming (1969) (38)
Multirate methods for ordinary differential equations (1974) (37)
Parallelism across time in ODEs (1993) (36)
Computing in the past with forward integration (2004) (35)
Sparsity structure and Gaussian elimination (1988) (34)
Massive parallelism across space in ODEs (1993) (33)
The Stability of Numerical Methods for Second Order Ordinary Differential Equations (1978) (33)
Manifold learning for parameter reduction (2018) (28)
Invariants and numerical methods for ODEs (1992) (28)
A simple set of test matrices for eigenvalue programs (1969) (24)
Waveform methods for space and time parallelism (1991) (24)
Feature grouping in moving objects (1994) (22)
Analysis and Computation of a Discrete KdV-Burgers Type Equation with Fast Dispersion and Slow Diffusion (2009) (21)
Projective Integration Methods for Distributions (2001) (21)
Automatic Multirate Methods for Ordinary Differential Equation (1980) (21)
Towards explicit methods for differential algebraic equations (2006) (21)
An equation-free approach to agent-based computation: Bifurcation analysis and control of stationary states (2012) (20)
Projective and coarse projective integration for problems with continuous symmetries (2006) (20)
High speed compilation of efficient object code (1965) (20)
The analysis of generalized backwards difference formula methods applied to Hessenberg from differential-algebraic equations (1991) (20)
Automatic methods for highly oscillatory ordinary differential equations (1982) (20)
An Introduction to Numerical Methods for ODEs and DAEs (1990) (18)
The Numerical Solution of Problems Which May Have High Frequency Components (1984) (17)
Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold (2012) (16)
Smooth Numerical Solutions of Ordinary Differential Equations (1983) (15)
Simulation: Conflicts between Real-Time and Software (1977) (15)
Data-Driven Reduction for Multiscale Stochastic Dynamical Systems (2015) (14)
Constraint-defined manifolds: A legacy code approach to low-dimensional computation (2005) (14)
Implementation of preconditioned s-step Conjugate Gradient methods on a multiprocessor system with memory hierarchy (1987) (14)
A Graphical Search for Stiffly Stable Methods for Ordinary Differential Equations (1971) (12)
The development of ODE methods: a symbiosis between hardware and numerical analysis (1987) (10)
Some remarks on inverses of sparse matrices (1985) (9)
Parallel Solution of ODEs (1990) (9)
Equation-free Model Reduction in Agent-based Computations: Coarse-grained Bifurcation and Variable-free Rare Event Analysis (2015) (9)
Manifold learning techniques and model reduction applied to dissipative PDEs (2010) (9)
An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients (2017) (9)
Introduction to Computer Science (1973) (8)
EFFICIENT STEP SIZE CONTROL FOR OUTPUT AND DISCONTINUITIES. (1984) (8)
Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations (1982) (8)
The Speed of Waveform Methods for Odes (1991) (8)
Numerical solution of ordinary differential equations at a remote terminal (1966) (7)
Initial value problems: practical theoretical developments (1979) (7)
Automatic multirate methods for ordinary differential equations. [Adaptive time steps] (1980) (7)
Coarse-Grained Descriptions of Dynamics for Networks with Both Intrinsic and Structural Heterogeneities (2017) (7)
On obtaining a consistent set of initial values for a system of differential-algebraic equations (1987) (7)
Boundary processing for Monte Carlo Simulations in the Gap-Tooth Scheme (2002) (6)
Accuracy increase in waveform Gauss Seidel (1989) (6)
Parameterization of non-linear manifolds (2012) (6)
Documentation for DFASUB: a program for the solution of simultaneous implicit differential and nonlinear equations (1973) (6)
Estimation of Errors and Derivatives in Ordinary Differential Equations (1974) (5)
On the acceleration of spatially distributed agent-based computations (2014) (5)
Numerical Software: Science or Alchemy? (1980) (5)
The Stability of Automatic Programs for Numerical Problems (1974) (4)
Programming and languages (1978) (4)
Treating a single, stiff, second-order ODE directly (1989) (4)
On-the-Fly Local Error Estimation for Projective Integrators (2006) (4)
DAEs: ODEs with constraints and invariants (1989) (4)
Selected Papers from the Second Conference on Parallel Processing for Scientific Computing, Norfolk, Virginia, USA, November 18-21, 1985 (1985) (4)
Optimization of the Address Field Compilation in the ILLIAC 2 Assembler (1964) (4)
Computer applications and algorithms (1986) (3)
Rational approximations by implicit Runge-Kutta schemes (1970) (3)
Manifolds defined by points: Parameterizing and boundary detection (extended abstract) (2016) (3)
Numerical methods for ordinary differential equations : proceedings of the workshop held in L'Aquila (Italy), Sept. 16-18, 1987 (1989) (3)
Singular implicit ordinary differential equations and constraints (1983) (3)
Proceedings of the 2nd conference on parallel processing for scientific computing (1987) (3)
Equationfree Modeling For Complex Systems (2005) (3)
Slow Manifold Integration on a Diffusion Map Parameterization (2011) (2)
Time varying radial basis functions (2014) (2)
Reverse Integration for Computing Stationary Points of Unstable Stiff Systems (2003) (2)
TOWARDS EXPLICIT METHODS FOR DAES (2006) (2)
Numerical computations: its nature and research directions (1979) (2)
Computation & cognition : proceedings of the First NEC Research Symposium (1991) (1)
Asynchronous integration of ordinary differential equations on multiprocessors (1989) (1)
Computing on Virtual Slow Manifolds of Fast Stochastic Systems 1 (2010) (1)
Real-time integration formulas with off-step inputs and their stability (1989) (1)
Iterative solution of linear equations in ODE codes. [Krylov subspaces] (1981) (1)
Implementation of s-step methods on parallel vector architecture (1987) (1)
Numerical integration in ordinary differential equations operating under ILLIAC II time-sharing system (1966) (1)
A simple example using equation-free computation. (2008) (1)
Computation And Cognition (1991) (1)
Computer systems research. Progress report, July 16, 1975--July 15, 1976. [Dept of Computer Science, Univ. of Illinois at Urbana-Champaign, for July 16, 1975 to July 15, 1976] (1976) (1)
Potential performance of methods for parallelism across time in ODEs (1990) (1)
An ill-conditioning problem with implicit integration (1969) (1)
Some matrix results for stable m-dimensional rotations (1974) (1)
Software systems research. Annual report, November 16, 1979-November 15, 1980. [Dept. of Computer Sciences, Univ. of Illinois, Urbana] (1980) (1)
Panel Discussion of Quality Software for ODEs (1976) (1)
Singular Solutions at Boundary Intersections in Two Dimensional Quasi-Linear Homogeneous Partial Differential Equations (1964) (0)
Note on the nonexistence of multivalue A-stable methods of order greater than two (1973) (0)
ODEs: is there anything left to do (1979) (0)
Error estimation and control in O.D.E. integration (1974) (0)
Computer organization and programming : with an emphasis on the personal computer (1985) (0)
Computational methods and software for differential equations and their applications: Annual report, December 1, 1986-November 30, 1987 (1987) (0)
Virtual Slow Manifolds: The Fast Stochastic Case (2009) (0)
R65-56 IBM System 360 Engineering (1965) (0)
AUTOMATIC MULTIRATE METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS (2012) (0)
Effect of variable mesh size on the stability of multistep methods (1973) (0)
Graphical Computer Aided Programming Systems (1969) (0)
Annual report, September 1, 1972--August 31, 1973 (1973) (0)
Programming in Pascal (1983) (0)
Invariants of fast solutions of KdV-Burgers Equations C (2009) (0)
USA-JAPAN COMPUTER CONFERENCE PROCEEDINGS, 1972. (2017) (0)
COMPUTER SYSTEMS RESEARCH. Annual Report, September 1, 1969--August 31, 1970. (1970) (0)
Numerical Solution of Differential Equations (Isaac Fried) (1980) (0)
ANNUAL REPORT, SEPTEMBER 1, 1970--AUGUST 31, 1971. (1971) (0)
Editor's Note (1979) (0)
Software systems research. Progress report, September 1, 1973--July 15, 1974 (1974) (0)
Coarse integration of bubble flows using lattice Boltzmann simulators (2003) (0)
Computer Systems Research Annual Report, September 1, 1967--August 31, 1968. (1968) (0)
Singular Shock Intersections in Plane Flow (1960) (0)
Special Section on Sparse Matrix Algorithms on Supercomputers (1989) (0)
Conference record of the 5th annual workshop on Microprogramming, MICRO 1972, Urbana-Champaign, Illinois, USA, September 25-26, 1972 (1972) (0)
Finding Stationary States of Noisy Processes (0)
A Note from the Editors (1985) (0)
Proceedings of the SIGNUM Meeting on Software for Partial Differential Equations, Moffitt Field, California, USA, December 8-9, 1975 (1975) (0)
Methods for oscillating problems (1977) (0)
TIME SHARING AT ILLINOIS: EXPERIENCE AND PLANS. Report No. 217. (1966) (0)
Discretization Methods for Stable Initial Value Problems (Eckart Gekeler) (1985) (0)
Are waveform methods suitable for parallel or vector computers (1988) (0)
Coarse Integration of Monte Carlo Simulations of Bacterial Chemotaxis (2002) (0)
Runge-Kutta Starters for Methods (1980) (0)
Explicit stiff stability via splitting and the parallel solution of ODE (1987) (0)
J ul 2 00 3 Coarse Projective kMC Integration : Forward / Reverse Initial and Boundary Value Problems (2008) (0)

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What Schools Are Affiliated With C. William Gear?

C. William Gear is affiliated with the following schools: