A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.
A topological asymptotic analysis for the regularized grey-level image classification problem
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.
Algorithm. 44. MIMUN. Optimization of one-dimensional multimodal functions in the presence of noise
Algorithm 65. Determination of the solution of an Abel integral equation
Algorithm 67. Determination of the solution of Abel integral equations, II
Algorithm 68. Determination of the solution of Abel integral equations, III
Algorithm 84. The choice of representative variables by stepwise regression
Algorithms. 47. ALPHA CHISQ. An algorithm for the chi-square test without application of critial values
Algorithms 73-76. Four algorithms for evaluation of improper integrals
Algorithms 80-81. Calculation of projections
An Algorithm for Generating Random Numbers With Binomial Distribution
An Algorithm for the Computation of the Exponential Spline.
Computer-Assisted Proofs and Symbolic Computations
We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems...
Concepts—An object-oriented software package for partial differential equations
Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such...
Concepts—An Object-Oriented Software Package for Partial Differential Equations
Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into ...
Dynamic systems with the nonzero initial conditions excited by the Dirac function
Explizite Konstruktion von linearen Mehrschrittblockverfahren
In der vorliegenden Arbeit wird für lineare Mehrschrittblock verfahren zur numerischen Lösung von Anfangswertaufgaben eine explizite Konstruktionsmöglichkeit angegeben. Sie ermöglicht es, zu einem gegebenen Stabilitätspolynom ohne Lösung eines linearen Gleichungssystems die Koefizienten des zugehörigen Blockverfahrens zu berechnen.
FLENS - a flexible library for efficient numerical solutions
Graphics card as a cheap supercomputer
The current powerful graphics cards, providing stunning real-time visual effects for computer-based entertainment, have to accommodate powerful hardware components that are able to deliver the photo-realistic simulation to the end-user. Given the vast computing power of the graphics hardware, its producers very often offer a programming interface that makes it possible to use the computational resources of the graphics processors (GPU) to more general purposes. This step gave birth to the so-called...
Householder's Method for Complex Matrices and Eigensystems of Hermitian Matrices.