A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES

By Kenneth Levenberg. 1944

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation (2019, methodology): “where τ ≥ 0 is the LM regularization (Levenberg, 1944; Marquardt, 1963).”
Deep learning in neural networks: An overview (2014, neutral): “Least-squares methods (Gauss– Newton, Levenberg–Marquardt) (Gauss, 1809; Levenberg, 1944; Marquardt, 1963; Newton, 1687; Schaback & Werner, 1992) and quasi-Newtonmethods (Broyden–Fletcher–Goldfarb–Shanno, BFGS) (Broyden et al., 1965; Fletcher & Powell, 1963; Goldfarb, 1970; Shanno, 1970) are…”
Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling (2018, methodology): “The Efficient PnP (EPnP) algorithm solves the problem using virtual control points [36].”
New Insights and Perspectives on the Natural Gradient Method (2014, background): “And before that have had a long history of application in the context of practical non-linear regression procedures (Tikhonov, 1943; Levenberg, 1944; Marquardt, 1963; Moré, 1978).”
Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both? (2019, methodology): “A training algorithm based on an approximate Newton’s method with a regularization strategy is the Levenberg-Marquardt method [124], [125], which yields good performance as long as the negative eigenvalues of the Hessian of the cost function are relatively close to zero.”
Relationship between freight accessibility and logistics employment in US counties (2013, methodology): “This software uses the Levenberg-Marquardt method to solve nonlinear regressions, which combines the steepest-descent method and a Taylor series based method (Levenberg, 1944; Marquardt, 1963).”
MAX‐DOAS O4 measurements: A new technique to derive information on atmospheric aerosols: 2. Modeling studies (2006, methodology): “A slightly modified version of equation (9) based on the method of Levenberg [1944] and Marquardt [1963] with a faster convergence rate is used here.”
Neural networks for pattern recognition (1995, methodology): “61) we arrive at the Levenberg-Marquardt approximation (Levenberg, 1944; Marquardt, 1963) or outer product approximation (since the Hessian matrix is built up from a sum of outer products of vectors), given by”
3D hand tracking by rapid stochastic gradient descent using a skinning model (2004, methodology): “When derivatives are available, nonlinear optimization problems are often solved by second-order gradient techniques such as the Levenberg-Marquardt algorithm [19, 20] or truncated quasi-Newton method like the BroydenFletcher-Goldfarb-Shanno (BFGS) algorithm [18].”
An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations (2018, methodology): “The Levenberg–Marquardt (LM) method [8,9], to overcome this difficulty, computes a trial step dk by dk = −(JT k Jk + λkI)−1JT k Fk, (2)”
Estimation of dimensionless parameters of Luikov's system for heat and mass transfer in capillary porous media (2002, methodology): “The Levenberg–Marquardt method [12, 13,18–20] is used as the minimization procedure of the leastsquares norm in order to estimate the parameters.”