The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points of the Spectrum.
The Convergence of two Numerical Schemes for the Navier-Stokes Equations.
The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization
The convergence rate of the Chebyshev semiiterative method under a perturbation of the foci of an elliptic domain.
The Convergence Rates of Expansions in Jacobi Polynomials.
The convex interpolation of histogram by polynomial splines: The existence theorem
The Coordinex Problem and Its Relation to the Conjecture of Wilkinson.
The correct use of the Lax–Friedrichs method
We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of the discussion, we give a recipe that ensures that the number of extrema within the discretized version of...
The correct use of the Lax–Friedrichs method
We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of the discussion, we give a recipe that ensures that the number of extrema within the discretized version...
The Coverage Model and Its Use in Image Processing
The cross-validation method in the polynomial regression.
The cross-validation method in the smoothing spline regression.
The Cubic Revisited.
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The -stability problem for real matrices
We give detailed discussion of a procedure for determining the robust -stability of a real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.
The equation and financial mathematics. II
This paper continues the research started in [J. Štěpán and P. Dostál: The equation and financial mathematics I. Kybernetika 39 (2003)]. Considering a stock price born by the above semilinear SDE with we suggest two methods how to compute the price of a general option . The first, a more universal one, is based on a Monte Carlo procedure while the second one provides explicit formulas. We in this case need an information on the two dimensional distributions of for where is the exponential...
The Defect Correction Principle and Discretization Methods.
The density of solenoidal functions and the convergence of a dual finite element method
A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The Derivation of Cubic Splines with Obstacles by Methods of Optimization and Optimal Control.