A Class of Methods for Solving Nonlinear Simultaneous Equations

By C. G. Broyden. 1965

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Citations in the corpus

Entropy Search for Information-Efficient Global Optimization (2011, methodology): “Popular algorithms for such settings include quasi-Newton methods (Broyden et al., 1965; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970), the conjugate gradient method (Hestenes and Stiefel, 1952), and stochastic optimization and evolutionary search methods (e.g. Hansen and Ostermeier (2001)), to…”
Deep Equilibrium Models (2019, methodology): “Both instantiations of DEQ use Broyden’s method [10] to avoid direct computation of the inverse Jacobian, as described in Section 3.1.3.”
A derivative-free line search and global convergence of Broyden-like method for nonlinear equations (2000, methodology): “In particular, for nonlinear equations involving a mapping with positive de nite Jacobian matrices, we propose a norm descent quasi-Newton method and establish its global and superlinear convergence.”
A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion (2002, unknown): “The updating method assumes that the change in the Jacobian matrix values between consecutive iterations is rank-one matrix (Broyden, 1965).”
Phoretic self-propulsion at finite Péclet numbers (2014, unknown): “12 of the solution and an estimate of the inverse of the Jacobian matrix J−1 n = [∇αF(αn)], a new estimate for both quantities is obtained as [10] α = α − J−1 n ·α, (65) J−1 n+1 = J −1 n + (∆α− J−1 n ∆F) · (∆α · J−1 n ) ∆αT · J−1 n ·∆α , (66)”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, background): “The function f is the two-dimensional modified Broyden tridiagonal function [48] [185].”
Simulation of planar flexible multibody systems with clearance and lubricated revolute joints (2010, methodology): “In this study, based on Arnold and Bruls’ work, the Broyden–Newton [ 53 ] approach is also introduced in to the iteration process.”
Calibration‐constrained Monte Carlo analysis of highly parameterized models using subspace techniques (2009, methodology): “Equations are presented that describe (1) how calibration can be formulated as subspace-based regularized inversion, (2) how postcalibration parameter error variance is calculated, (3) the projection of stochastic parameter values onto the calibration null-space, and finally, (4) Broyden’s rankone u”
Combining model-based policy search with online model learning for control of physical humanoids (2016, background): “The result is a linear system that lends itself to efficient rank one updates [1], [10]”
Historical development of the BFGS secant method and its characterization properties (2009, methodology): “In 1959, Davidon [30] introduced a new method for minimization using the secant idea and in 1965, Broyden [12] presented a new method for solving systems of equations using the secant idea.”
Space mapping: the state of the art (2004, methodology): “An initial approximation to can be taken as , the identity matrix. can be updated using Broyden's rank one formula [36] (18) When is the quasi-Newton step, (18) can be simplified using (16) to (19)”