** Number 1, pp. 1-108 Number 2, pp. 109-206 Number 3, pp. 207-323 Number 4, pp. 325-421**

**Bogdanov V.V., Volkov Yu.S. Selection of parameters of generalized cubic splines with convexity preserving
interpolation **(

equations with column diagonal dominance with respect to knot values of the second derivative of a spline. The non-negativity conditions of the solution for such systems are found. The general scheme for choosing tension parameters of the generalized splines for convexity-preserving interpolation is offered. The resulting spline minimally differs from the classical cubic one and coincides with it if sufficient convexity conditions for the last one are satisfied. The algorithms specified are considered for different generalized cubic splines such as rational, exponential, variable power, hyperbolic splines and splines with additional knots.

Kretinin A.V.

The weighted residuals method based on neuronet approximations for simulation

of hydrodynamics problems

The algorithm was tested on solving the two-dimensional Navier-Stokes equations. The algorithm is applied to modeling the variable mass flow.

Mikhailenko B.G., Reshetova G.V.

The numerical-analytical method of solving the problem of seismic and acoustic-gravity wave propagation for the inhomogeneous model Earth-Atmosphere

Moghrabi I.A.R.

Multiple update multi-step methods for unconstrained optimization

other existing methods at minimal extra storage and computational overhead.

Rozhenko A.I.

On calculation of scalar products of B-splines

calculations of integrals in the Gram matrix is proposed. The modified algorithm is nearly two times faster than the Gauss quadratures and the full recursion algorithm.

Shishkin G.I.

Higher-order accurate method for a quasilinear singularly perturbed elliptic convection--diffusion equation (

Urev M.V.

The convergence of finite element method for axially symmetric magnetostatic problem

**Amelkin V.A.**

**Recalculation, numbering and generation of serial sequences with detached natural series **
(*in Russian*), pp.109-121

The sets of integer-valued serial sequences of the length *m*, whose structure is determined by limitations on the quantity, total length and permitted lengths of natural series, as well as on lengths of
separating 0-series are considered. The cases when
lengths of boundary series may not satisfy the given
constraints are considered as well. Exact solutions to
problems of recalculation, coding and generation are obtained for such sets.

**Key words:**
series, sequence of series, restrictions, enumeration.

**Godunov S.K., Selivanova S.V. Experiments on using the resonance effect for spectral analysis
of finite-dimensional skew-symmetric operators **(

An algorithm of spectral analysis for skew-symmetric matrices based on using the resonance effect is proposed and studied. Its application to computation of oscillation spectra for conservative systems of hyperbolic equations is discussed on the example of three-dimensional linear elasticity.

A problem of flow through semipermeable obstacle

This paper deals with mathematical analysis of a potential flow through a thin semipermeable obstacle. The boundary value problem is characterized by the inequality type conditions imposed on a non-smooth component of the boundary. We prove solvability of the boundary value problem and analyze the solution properties. Using boundary elements, an optimization technique for the numerical solution of the problem is proposed. Numerical results for test problems are presented.

The orthogonal and the nodal polynomials

The polynomials

Conditional optimization of discrete-stochastic numerical procedures with cubic splines applied

In this paper, the discrete-stochastic numerical procedures of the global function approximation are considered. The procedures are built to approximate the solution to an integral equation of the second kind using the Streng-Fix approximation with cubic B-splines as basis functions. In the case of using cubic splines, a discrete component of the approximation error has a higher order with respect to the grid step as compared to the well-studied case of the multi-linear approximation. Moreover, the property of "error concentration in grid nodes'' is proved to hold for approximation with the cubic splines as well. This is because the coefficients of the approximation are, in fact, linear combinations of the function values in grid nodes. The above properties provide the upper bounds for the total approximation error. Finally, for the investigated discrete-stochastic procedures, the conditionally-optimal parameters are calculated that minimize computational costs for the procedures with the fixed error upper bounds.

Periodic interpolation with a minimum norm of the

In this paper, the interpolation problem for periodic data with a bounded

Inner estimation of solution sets to non-negative interval linear systems

This paper presents a new technique for constructing the maximum (with respect to an inclusion) inner estimates of the solution sets to the interval linear equations systems having non-negative matrices, based on

**Bazanov P.V., Djosan O.V. Methods of face feature extraction of the human identification
problem **(

This paper offers three different methods that are used to extract information features from a face image. We suggest effective modifications of the feature extraction methods based on the principal component analysis, wavelets, hidden Markov models.

The human face recognition experiments were carried out using the database with normalized faces. These experiments have shown advantages and disadvantages of the methods proposed.

Visualization of city environment by the plenoptic method

We describe an image-based rendering algorithm that allows the visualization of large spatial scenes. Images taken by an ordinary digital camera are used as inputs. These images are transformed into panoramic views, which are 4D parameterization of the full plenoptic function for further storing. Using a simple proxy geometry, we can create the novel view from these structures.

The cases, when our approach can be used, are formulated. The results of our algorithm for both synthetic and real scenes are demonstrated.

The impulse-based method for the simultaneous resolution of collisions between rigid bodies

The paper proposes an enhanced version of the impulse-based method for the numerical simulation of collisions between rigid bodies. This approach makes it possible to resolve several collisions simultaneously, allows for inelastic collisions with energy loss, and supports assembly constraints.

On constructing the shortest circuits on a set of line segments

This paper deals with the problem of defining the Hamiltonian cycle on segments by the ant colony algorithm. Parameters and properties of this algorithm as applied to the cutting chart for the NC machine and an arbitrary set of segments are studied.

Extending RANSAC-based estimators to handle unknown and varying noise level

The robust parameter estimation methods are a general tool in computer vision, widely used for such tasks as multiple view relation estimation and camera calibration. In this paper, a new robust maximum-likelihood estimator AMLESAC is presented. It is a noise-adaptive version of the well-known MLESAC estimator. It adopts the same sampling strategy and seeks the solution to maximize the likelihood rather than some heuristic measure. Unlike MLESAC, it simultaneously estimates all the noise parameters: inlier share

Modeling and evaluation of the Stewart platforms

This paper presents an efficient algorithm for solving the forward kinematics problem and an application for the motion modeling of the Stewart platforms. The developed application is able: (i) to solve the forward kinematics problem with a given accuracy; (ii) to calculate the trajectory of a tool positioned on the mobile platform; (iii) to calculate a possible deviation of the tool from a nominal position or a trajectory if lengths of the legs are varying within given tolerances; (iv) to detect the crossing of the legs during motions of a mobile platform. A projected movement of the Stewart platform can be specified by explicit parametric expressions for platform coordinates or by the spline-interpolation of trajectory nodes. The

computational core of the application is based on the new efficient algorithm, which provides the minimum number of unknowns and the quadratic convergence rate even if two subsequently calculated positions are far apart.

Integration methods in the problem of modelling a fabric based on the particles method

This paper describes a fabric simulation system. On the basis of the method of particles with allowance for physical properties of a fabric, the model and the algorithm for modelling the behaviour of a fabric on the surface of a rigid polyhedral object are developed. A comparative analysis of some different integration methods is made. And some results of the simulation are presented.

Skeletonization of a multiply-connected polygonal domain based on its boundary adjacent tree

The problem of a continuous skeleton construction for a multiply connected polygonal domain is considered. The polygonal domain is a closed one, whose boundary consists of a finite number of simple polygons. The

Volumetric algorithm for 3D surface generation

This paper describes the process of creating a single 3D model from a number of previously aligned scans. Using the volumetric algorithm makes the solution of this problem intuitively clear and easy for implementation. In addition, it describes the data structure decreasing the memory requirement needed for processing large models.

The post-processing algorithms for images and video

The blockness and ringing are the two main types of artifacts occurring as a result of the use of block image compression and video coding algorithms for a high compression ratio. Today, most of applied deblocking and deringing algorithms are time-consuming and can not be used for devices which perfect coding/decoding in the real time mode. The adaptive deblocking post-processing algorithm is offered in this paper. The algorithm allows one to underline textures without changing them and, also, eliminates ringing artifacts on the decoded images. The offered algorithms decrease disadvantages of image coding and give good contours and real textures keeping for real edges in decoded images. Moreover, the developed methods are not time-consuming and may be integrated in any type of processors. Preliminary experiments have shown that for 352x288 images, the working time was about 0.31 ms, and with a special optimization these algorithms may really work in real time (25-30 frames per s).

**Artemiev S.S., Yakunin M.A.**

**Analysis of the number of sale/purchase signals for trade
algorithms **(*in Russian*), pp.325-334

We investigate probability characteristics of the results of the trade for trade
algorithms. The latter are based on smoothing a price series by exponential
moving average. In the case of the model of a price series with a Gaussian
distribution of price increments, the parametric analysis of mathematical
expectation of the number of sale/purchase bargains and probability of making a
bargain is carried out.

**Key words:** trade algorithm, the number of bargains, moving average.

**Fedotov A.V. Forecasting the bank resources dynamics by Monte Carlo method **(

Bank liquidity is predicted on the basis of mathematical model of bank account by Monte Carlo method. Various statistical characteristics of bank profit and risk are calculated.

On a smooth volume approach, integral conservation law, and upwind scheme with monotonic reconstruction

This paper presents a smooth volume approach - an alternative to smooth particle formalism. The proposed approach is based on approximation of integral conservation law and can be viewed as a generalization for the finite volume method. To provide insight into properties of smooth volume schemes, a hypothesis is presented. On its basis, an extension technique for the development of smooth volume schemes is suggested. Using this technique, the finite volume upwind and the Godunov schemes with monotonic reconstruction are generalized to smooth volume schemes. The hypothesis, the technique and the resulting schemes are tested by applying them to gasdynamics shock tube problems. Precise and monotonic calculation results verify validity of our theory and properties of the schemes developed.

Preconditioning by multilevel methods with locally modified grids

Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This ``locally modified'' grid possesses several significant features: this triangulation has a regular structure, generation of the triangulation is rather fast, this construction allows the use of multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving grid elliptic boundary value problems are based on two approaches: the fictitious space method, i.e., reduction of the original problem to that in an auxiliary (fictitious) space, and the multilevel decomposition method, i.e., construction of preconditioners by decomposing functions on hierarchical grids. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh size. The construction of the grid and the preconditioning operator for the three-dimensional problem can be done in the same manner.

On a numerical method for problem of a non-stationary flow of incompressible

fluid with a free surface

A numerical method for obtaining approximate solutions to equations describing a non-stationary motion of an ideal liquid with free boundary in a gravitational field is constructed. The convergence is proved, provided that a smooth solution exists. An efficient numerical scheme is proposed.

Approximation by local exponential splines with arbitrary nodes

For the class of functions

and generalized convexity of the data (values of a function

The optimum in order method of solving conditionally-correct problems

Necessary and sufficient conditions, which ensure sets of the Banach spaces to be classes of correctness are obtained. The

concept of solution method of conditional-correct problem is given. The quantitative characteristic of its accuracy on an

appropriate class of correctness is determined. The obtained results are used for solving one inverse problem of solid-state

physics.

Numerical investigation of a model problem for deforming an elastoplastic body with a crack under non-penetration condition

The Lam$\acute{e}$ system is considered in a two-dimensional domain with a crack. The Dirichlet and the Neuman

conditions are held on the exterior boundary, and non-penetration condition is assumed to be on a crack. The convolution

product of the deviator of the stress tensor is restricted by a certain constant within the domain. Thus, we have a model problem for deforming an ideal elastoplastic body with a crack (the Henky model) subject to the Mises yield criterion. Simultaneously, the non-penetration condition is held on a crack. The problem is formulated as a variational one. We find a displacement vector as solution to minimization problem for the energy functional over a convex set. Discretization of the problem is provided by a finite element method. Examples of calculation are obtained using the Udzava algorithm.