Application of Rothe's method to evolution integrodifferential equations.
A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from several shotpoints,...
To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose...
We propose an adaptation of the partitioning method for determination of the Moore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant...
An extension of the Rasch model with correlated latent variables is proposed to model correlated binary data within families. The latent variables have the classical correlation structure of Fisher (1918) and the model parameters thus have genetic interpretations. The proposed model is fitted to data using a hybrid of the Metropolis-Hastings algorithm and the MCEM modification of the EM-algorithm and is illustrated using genotype-phenotype data on a psychological subtest in families where some members...
We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion...