Geodesic

Sommaire du Fascicule no. 1

Errata
Minimization of computational algorithms in certain transformations of matrices
p. 3-13
A method of differential descent for solving non-linear systems
p. 14-32
A non-linear extremal problem
p. 33-51
A gradient method for solving a class of optimal control problems
p. 52-61
Regularization of difference schemes
p. 62-93
Solution of integral equations of the first kind with a product type kernel
p. 94-112
Some problems in the mathematical theory of the critical state of a reactor
p. 113-127
The Cauchy problem for small oscillations of a viscous liquid in a weak field of mass forces
p. 128-146
Proof of the convergence of Sheleikhovskii's method for a problem with transportation constraints
p. 147-156
Solution of systems of linear equations
p. 157-160
An iteration process for the solution of a finite-dimensional contact problem
p. 160-163
On finding mor precisely the position of points of a matrix spectrum
p. 163-164
Interpolation methods for calculation of simple and multiple real roots of functions
p. 165-167
Finding the right-hand boundary for the zeros of an exponential polynomial
p. 167-172
Calculations of the Ritz and Galerkin coefficients by the Monte-Carlo method
p. 172-177
On a new form of Fourier series and the choice of best Fourier polynomials
p. 177-185
Construction of cubature formulas and orthogonal polynomials
p. 185-189
Plane nets of integration
p. 189-196
On asymptotic representations of spheroidal functions
p. 196-198
Stability of solution of a functional equation of dynamic programming
p. 199-204
On a method of unconditional optimization in problems of convex programming
p. 204-208
On some small parameter systems
p. 208-214
Uniform stability of a six-point scheme of higher order accuracy for the heat equation
p. 214-218
The accuracy of measurements and the existence of a solution of the problem of radioactive decay
p. 218-222
The current distribution on the surface of a thin impedance dipole in the form of a solid of revolution
p. 223-226
Список неясных мест в АЛГОЛе-60
p. 227-235
Letter to the editorial board
Einführung in die Funktionentheorie: Nevanlinna R. and Paatero V. Birkhauser, Basel-Stuttgart, 1965
p. 235-236
Magnetohydrodynamics: Jeffrey, A. Oliver Boyd, Edinburgh, 1966
p. 236-237
Einführung in die algorithmische Sprache ALGOL: Kerner, I. O. and Zielke, G. Leipzig, 1966
p. 237-239
Bibliography
p. 239-240

Sommaire du Fascicule no. 2

The statistical investigation of round-off errors in numerical integration on a fixed point computer
p. 243-258
An existence theorem for optimal control in the Boltz problem, some of its applications and the necessary conditions for the optimality of moving and singular systems
p. 259-283
Reduction of a multi-point problem for a system of differential equations to the Cauchy problem by the method of orthogonal transformations
p. 284-295
On the stability in $W_2^2$ of schemes with a decomposed operator
p. 296-302
Properties of an iteration process
p. 303-311
Splitting operator difference schemes for general second order $p$-dimensional parabolic equations with mixed derivatives
p. 312-321
The theory of electron plasma non-linear oscillations
p. 322-347
Electrostatic distribution over a thin segment of a hyperboloid
p. 348-356
Numerical methods for solving some problems in the theory of heavy liquid motion
p. 357-366
Synthesis of round-trip trajectories closely encircling the moon
p. 367-388
Calculation of supersonic flow round sharp asymmetric bodies
p. 389-400
On some extremal problems for matrix norms
p. 401-404
Symmetrized Seidel method for non-selfconjugate systems of linear algebraic equations
p. 404-405
Inversion of matrices of special form
p. 406-408
Formulea for evaluating the fist 63 Lamé functions
p. 409-411
Closure of two computational algorithms based on the idea of orthogonalization
p. 411-416
Correct methods of solving problems of optimal control
p. 416-423
Formulation of higher-order iteration processes
p. 423-424
Some iteration methods of solving non-linear equations with non-differentiable operators
p. 425-429
Algorithms of minimization of strictly convex functionals
p. 429-431
Investigation of Maxwell's equations using $F$-monogenic functions
p. 431-436
The phase method of determining eigenvalues for the Schrödinger equation
p. 436-440
The occurrence of singularities in solutions of the non-steady seepage equation
p. 440-444
Aerodynamic characteristics of a sphere and a blunt cone in a flow of highly rarefied gas
p. 444-452
Numerical solution of plane problems in the theory of elasticity
p. 452-460
Determining the time characteristics in network planning with random evaluations of the length of operations
p. 460-466
Multidimensional Gaussian distributions: Miller, K.S. John Wiley and Sons Inc., New York-London-Sydney, VIII + 129 pp., 1964
Differentiation und Integration ausgewahlter Beispiele. Aufl. 6. Leipzig, B. G. Teubner, 1964
p. 467-468
Introduction to calculus and analysis. vol. 1: Courant, R. and John, F. New York–London–Sydney, Intersci. Publs. A div. of John Wiley and Sons, Inc., VII + 661 pp., 1965
Error propagation for difference methods: Henrici, P. New York-London. John Wiley and Sons, Inc., VI + 73 pp.,
p. 468-469
Coulomb Wave functions. Roy. Soc. Math. Tables. vol. II: Curtis, A.R. Cambridge, Cambridge Univ. Press, XXXV + 209 pp., 1964
p. 469-470

Sommaire du Fascicule no. 3

Approximate solution of linear operator equations in Hilbert space by the method of least squares. II
p. 475-496
On the stability in a uniform metric of sets of difference equations
p. 497-509
On the stability in $C$ of the Cauchy problem for difference and partial differential equations
p. 510-540
On the solution of boundary value problems by iterative methods
p. 541-550
The maximum principle and boundary $\alpha$-estimates of the solution of the first boundary value problem for a parabolic equation in a non-cylindrical region
p. 551-567
The solution of a non-stationary problem of diffraction at an impedance wedge using tabulated functions
p. 568-579
The solution and investigation of some electrochemical problems by the method of straight lines
p. 580-593
The non-symmetric flow round the front part of a body of revolution due to a supersonic stream of an ideal or real gas
p. 594-608
A numerical method of solving the problem concerning the motion of a heavy liquid over uneven ground
p. 609-619
A relaxation method of finding a common point of convex sets and its application to the solution of problems in convex programming
p. 620-631
Pseudorandom numbers for the simulation of Markov chains
p. 632-643
Remarks on finding the eigenvalues and eigenvectors of matrices which arise in the application of Ritz's method or in the difference method
p. 644-647
Estimates of linear functionals for the solution of certain inverse problems
p. 648-654
The solution of non-linear algebraic and transcendental equations in the complex plane
p. 654-661
On the asymptotic behaviour of confluent functions
p. 661-667
On the calculation of functionals in the solutions of linear equations of the first kind
p. 667-672
A general method of constructing regularizing algorithms for a linear incorrect equation in Hilbert space
p. 672-677
Investigating the method of straight lines for non-linear elliptic equations
p. 677-680
On the application of optimal control theory in problems of heat conduction
p. 681-685
On the collision of atoms with a crystal surface
p. 685-691
A method of solution of the wave equation with additive potential
p. 691-694
Periodic solution of the standard equations for the motion of a viscous liquid
p. 694-698
Analysis of magnetogasdynamic flow
p. 698-704
Approximation methods in the space of integer functions in the solution of “bottleneck” problems
p. 704-710
Generation on an electronic computer of random numbers with exponential distribution
p. 710-713
The first all-union conference on monte carlo methods: Novosibirsk, 17–21 November 1966
p. 714-716
Cours d'automatique théorique: R. Paullu De La Barriere. Paris, Dunod, 1966, XIV + 404 pp.
p. 716-717
Fundamental methods in hydrodynamics. Vol. 3 of “Methods of computational Physics”: Eds. B. Alder, S. Fernbach and M. Rotenberg. New York–London, Academic Press, 1964, XII + 336 pp.
p. 717-718
Hypersonic flow theory, Vol. 1. Inviscid flows: W. D. Hayes and F. R. Probstein. New York–London, 1966, XV + 602 pp.
p. 719-720

Sommaire du Fascicule no. 4

Galerkin's perturbation method and the general theory of approximate methods for non-linear equations
p. 723-751
The convergence of the method of false perturbations for calculating eigenvalues
p. 752-763
The structure of matrices which are the inverse of the correlation matrices of random vector processes
p. 764-773
On the application of Newton's method in a singular case
p. 774-783
On the distribution of points in a cube and the approximate evaluation of integrals
p. 784-802
The “sweep” method for solving difference equations
p. 803-812
$P_{NI}$-equations
p. 813-824
Study of the solution of the nonstationary problem of plane wave diffraction at an impedance wedge
p. 825-835
Asymptotic properties of the energy distribution of neutrons slowed in an infinite medium
p. 836-851
An approach to the numerical solution of problems of mathematical physics
p. 852-858
Operation of Laval nozzles in undesigned modes
p. 859-866
Certain relations for the characteristic numbers of matrices
p. 867-869
A method for solving systems of nonlinear algebraic and transcendental equations
p. 869-874
On restoring functions by the regularization method
p. 874-881
Minimaxes of Lebesgue functions of Lagrange interpolation with equidistant base-points
p. 881-885
Asymptotic expansion of a class of definite integrals
p. 885-888
Radon's paper on the cubature formula
p. 889-891
Convergence of a collocation type method for ordinary differential equations
p. 892-894
Solution of boundary value problems for Laplace's equation by the method of conformal grids
p. 895-899
Use of the Runge–Kutta method for solving fredholm-type integro-differential equations
p. 899-905
Number of arithmetical operations necessary for the approximate solution of Fredholm integral equations of the second kind
p. 905-910
Methods of determining the surfaces temperature of a body
p. 910-914
Monte-Carlo calculation of derivatives of functionals from the solution of the transfer equation according to the parameters of the system
p. 915-919
The possibility of stationary neutron distributions in a power reactor
p. 920-923
Solution of boundary layer equations in the neighbourhood of the critical point
p. 924-929
Calculation of a boundary layer with chemical reactions along the generators of a body of revolution
p. 929-933
Supersonic flow round a blunt cone, allowing for radiation
p. 933-937
Second approximation differential equations for turbulent fluid motions
p. 937-943
An ALGOL-60 translator for the Minsk-1 computer
p. 943-946
Effectiveness of the method of mathematical expectations for a certain class of problems
p. 946-953
Evaluation of dose derivatives by the Monte Carlo method for optimizing protective screen shape and composition
p. 953-957
Discourse on Fourier series: C. Lanczos, Edinburgh–London, Oliver and Boyd, Ltd., 1966, VIII + 255 pp.
p. 958-959
Introduction to basic FORTRAN programming and numerical methods: W. Prager, New York–Toronto–London, Blaisdell Publ. Co., 1965, XII + 203 pp.
p. 959-960

Sommaire du Fascicule no. 5

Mathematical methods and scientific progress
p. 963-964
The asymptotic distribution of rounding off errors in linear transformations
p. 965-976
On the speed of convergence of approximate methods in the eigenvalue problem
p. 977-987
Total error estimate for the solution of a non-linear operator equation by simple iterations
p. 988-1000
Asymptotic representations for prolate spheroidal functions
p. 1001-1010
On the optimal speed of integrating analytic functions
p. 1011-1020
The computation of tables of roots and weights of Hermite and Laguerre polynomials for $n=1(1)101$
p. 1021-1030
Computations ofj conformal mappings and the construction of difference nets
p. 1031-1059
On the solution of nonlinear pursuit problems
p. 1060-1077
Asymptotic form of the solutions of a second order linear differential equation containing a complex parameter
p. 1078-1085
A method for introducing a parameter when solving boundary value problems for second-order nonlinear ordinary differential equations
p. 1086-1095
Classes of stable schemes
p. 1096-1133
Solution of a three-dimensional problem of the theory of elasticity by Ritz's method
p. 1134-1143
The method of small parameter in a boundary value problem for a system of Oseen
p. 1144-1166
One method of finding the maximum eigenvalue of a symmetric matrix
p. 1167-1171
Uniform polynomial approximations of functions of one variable
p. 1171-1176
Impossibility of the “gradient catastrophe” for slightly non-linear systems
p. 1176-1179
Solution of Dirichlet's problem for Laplace's equation by the method of statistical tests
p. 1179-1186
Use of Stieltjes' moments
p. 1186-1193
Note in connection with a criticism of Bellman's equation
p. 1193-1198
Resonance interaction of a charge with a three-dimensionally periodic magnetic field in the non-paraxial case
p. 1199-1202
Problem of the three-dimensional flight of a spacecraft to the orbits of the outer planets
p. 1202-1205
Error in digital computation: Ed. L. B. Rall, New York–London–Sydney, John Wiley and Sons Inc., Vol. I., 1965, IX + 324 pp., Vol. II, X + 288 pp.
Asymptotic expansions for ordinary differential equations: W. Wasow. New York–London–Sydney, John Wiley and Sons Inc., 1966, XI+362 pp.
p. 1206-1207
Bibliography
p. 1207-1208

Sommaire du Fascicule no. 6

The method of projections for finding the common point of convex sets
p. 1211-1228
The asymptotics for small $\varepsilon$ of the solution of the equation $u_t+(\varphi(u))_{x}=\varepsilon u_{xx}$, corresponding to a rarefaction wave, in the degenerate case
p. 1229-1236
The asymptotics of the eigenfunctions of the Laplace operator, concentrated near the boundary of a region
p. 1237-1249
The iterated $KP$-method
p. 1250-1269
Solution of the Fredholm equation of the first kind in a statistical ensemble of smooth functions
p. 1270-1284
The diffraction of the field of dipole radiation by two spheres
p. 1285-1297
The asymptotic spectral function of the Schrödinger equation
p. 1298-1319
The Cauchy–Poisson problem of waves on the surface of a viscous fluid of finite depth
p. 1320-1333
A difference method for solving boundary value problems of the axially symmetric equations of unsteady filtering
p. 1334-1345
On the implementation of recursive procedures
p. 1346-1357
The penalty method in linear programming and its realization on a computer
p. 1358-1366
The stability of linear equations on a compactum
p. 1367-1370
Incomplete Lipschitz–Hankel integrals
p. 1370-1374
Remark on the approximation of functions by polynomials
p. 1374-1375
Numerical differentiation by means of Chebyshev polynomials orthonormalized on a system of equidistant points
p. 1375-1379
Resonant motions in a substantially non-linear system with one degree of freedom in the critical case
p. 1379-1385
A matrix algorithm for solving linear differential equations and systems
p. 1385-1392
The spectrum of a family of difference operators over functions on a mesh graph
p. 1392-1398
The Bubnov–Galerkin method
p. 1398-1402
Solution of the single-velocity neutron transport equation in a spherically symmetric medium
p. 1402-1406
A method for solving the nonstationary transport equation
p. 1406-1413
The wave resistance of a viscous fluid of finite depth
p. 1413-1416
Diffusion in a mixture of ideal gases
p. 1416-1422
A diffusion problem in a two-medium system
p. 1423-1429
Numerical methods of algebra (theory and algorithms). Chislennye metody algebry (teoriya i algoritmy):
p. 1430-1431
On approximation theory: Eds. P. L. Butzer and J. Korevaar, Basel-Stuttgart, Birkhäuser, 1964, XVI+261pp.
p. 1431-1432
Nonlinear Partial Differential Equations in Engineering (Math. Sci. and Engineering, Vol. 18): W. F. Ames, New York–London, Academic Press, 1965, XII+511 pp.
p. 1432-1434