We consider possibly stiff and implicit systems of ordinary differential equations (ODEs). The major difficulty and computational bottleneck in the implementation of fully implicit Runge–Kutta (IRK) methods resides in the numerical solution of the resulting systems of nonlinear equations. To solve those systems we show that the use of inexact simplified Newton methods is efficient. Linear syste...

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demons...

To solve the problem of relative camera pose estimation, a method using optimization with respect to the manifold is proposed. Firstly from maximum-a-posteriori (MAP) model to nonlinear least squares (NLS) model, the general state estimation model using optimization is derived. Then the camera pose estimation model is applied to the general state estimation model, while the parameterization of ...

In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the dens...

We present methods for the quantitative analysis of brain growth based on the registration of longitudinal MR image data with the use of Jacobian determinant maps to characterise neuroanatomical changes. The individual anatomies, growth maps and tissue classes are also spatially normalised in an 'average space' and aggregated to provide atlases for the population at each timepoint. The average ...

We describe a method to compute invariant tori in phase space for classical non-integrable Hamiltonian systems. Our procedure is to solve the Hamilton-Jacobi equation stated as a system of equations for Fourier coefficients of the generating function. The system is truncated to a finite number of Fourier modes and solved numerically by Newton’s method. The rerulting canonical transformation ser...

A technique is presented in order to evaluate the probability of failure in analytical form instead of approximation methods like FORM/SORM and no series expansion is involved in this expression. This technique is based on the Finite Element Method to obtain the expression of the response of stochastic systems, and the transformation of random variables to obtain the probability density functio...

We prove that any C transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller [37] for maps of the interval with negative Schwarzian derivative. We also sh...

Hopf bifurcations in problems with O(2) symmetry are considered. In these problems, the Jacobian matrix is always singular at the circle of Z2 symmetric steady state solutions. While a couple of imaginary eigenvalue cross the imaginary axis, the Hopf bifurcation is not of standard type. The canonical coordinates transformation is used for removing the zero eigenvalue and converting the problem ...

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian ne...