The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss–Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Furthermore, adding a regularization term results in replacing the Gauss–Newton method, which may diverge, b...

This paper introduces a computationally e cient Gauss-Newton type adaptation algorithm for parallel-cascade realizations of truncated Volterra systems with arbitrary, but nite order nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. The complexity of our system is comparable to the c...

This paper describes a Gauss-Newton-based algorithm for the bundle adjustment problem with functional constraints (GNC). The GNC algorithm has superior theoretical convergence properties compared to the conventional bundle algorithm. Both algorithms were applied to simulated measurements of a sphere with 2–3 cameras and 4–9 points. For 2 cameras and 4–5 points, the GNC converged in substantiall...

Newton, in an unauthorized textbook, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Newton did not want to publish, that Euler did not recommend, that Legendre called “ordinary,” and that Gauss called “common” — is now named after Gauss: “Gaussian” elimination. (One suspects, he would not be amused.) Gauss’s...

X iv :m at h/ 00 04 18 7v 1 [ m at h. H O ] 1 A pr 2 00 0 Journal of Nonlinear Mathematical Physics 2000, V.7, N 2, 244–262. (Re)-Examining the Past q-Newton Binomial: From Euler To Gauss Boris A. KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received March 6, 2000; Accepted April 7, 2000 Abstract A counter-intuitive result of Gauss ...