SCIENTIFIC ABSTRACT TIKHONOV, A.N. - TIKHONOV, A.Y.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001755620001-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 16, 2001
• Sequence Number: 1
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

TIKHONOV, A.N.; ENENSHTEYN, B.S.
A method for determining the depth of the crystalline bam from
the phase curves of electromagnetic frequency soundings. Dokl.
AN SSSR .145 no.ls89-92 J1 162. (KIRA 15:7)
1. Hagnitnaya laboratoriya AN SSSR. 2. Chlen-korrespondent
AN SSSR (for Tikhonov).
(Sounding and soundings) (Geology, Structural)

S'/208/63/003/001/004/013
(/0
B112/B1.02
AUTHORS: Tikhgno . A. N.,.Samarskiy, A. A.,,j(moscow)
TITLE:, Homogeneous difference schemes with a high degree of
accuracy over non-uniform nets .
PERIODICAL: Zhurna~ vychislitel-Inoy matematiki i matematiche.9koy fiziki,
v. 3, ho. 1, 1963, 99-108
TEXT: This paper is a continuation of previous_~paperse (Zh.vychiaL.mdea.i..
matem. fiz., 1961, 1, No 1, 5-64; and No. 3, 425-440), the fundamental
estimates of which are shown to be valid without the additional conditions V
0 M h /h ljh;lo,~ho.. (2)
1N i+1 i\~ M2'
The accuracy of zero-rank schemes is characterized.by the mean square
step N
1, (1,h2)1/2 Ohi) 1/2.
NJ 2 ' 1
( j!q 2 ).
It amounts to 0 : The results of another paper by the same authors
Card 1/2 ; 2

S/208/63/003/001/004/013
Homogeneous difference schemes with ... B112/B~102
(~h. vychisl. matem. i matem. fiz., 1962, 2, No- 5, 812-832) concerning
the accuracy of standard schemes over non-uniform nets are improved.
SUBMITTED: September 29, 1962
Card 2/2

S12081631003100110111013
B112/B102
AUTHORS: Tikhonov, A. N., Gorbunov, A. D. (Mopcow)
TITLE: asymptotic estimates of error for a method of the Runge-Xutta
ype
PERIODICAL: Zhurnal vychislitelonoy matematiki i matematicheskoy fiziki,
V. 3, no. 1, 1963, 1'95-197
TEXT: Approximate solutions of the Cauchy problem
dy/dx = f(x,y), y(x 0) - Yo (1)
by means of a formula of the Runge-Kutta type are considered. It is
Bhown that the error satisfies the inequality
xk-xo- . .......
O(hG)E- f - exp NLd ~ + 0(h)"111
jjdk 11 1 0
if the function f is continuous and has continuous derivatives of the a-th
order. Asymptotic expansions of the error.are derived.
SUBIAIT~ED: April 9, 1962
Card 1 1

V,ROXEOV.SIXIY~ Yu.N.;_q ij
_kT,OflCvj A. ~
F.L. Burmistro-7; on t-p occasion of his 75th birtnp-i.
Zhur. nauch. i prikl. fot- i kin, 8 n0.(".4'75 N-D 16'3.
(MrRA 17~1)

TIKHONOV, A.N.; SAMARSKIT, A.A.
Stability of difference schemes. Dokl.IN SSSR 149 no.33529-531
Mr 163. (MIRA 16:4)
1. Chlen-korrespondent AN SSSR (for Tikhonov).
(Difference equations)

L 14363-63 Mi (d)/FCC WIMS AFFTC IJP(C)
ACCESSION NR: AP3003840 3/002a/63/:L51/003/0501/05o4
AUTHOR: _Tikhono~U A. N. -(Corr. me6. AS, SSSR)
TITLE: Solution of incorrectly stated problems and method of
regularity -
SOURCE: AN SSSR. Doklady*, v. 151, no. 3, 1963, 501-504
TOPIC TAGS: Fredholm equation, ificorrectly stated problem
ABSTRACT: An example of an incorrectly stated problem is
Fr edhol.1711 sequation of th--- first -kind -where a-solution-is
7 j~equired for the unknown function z(s) given the absolute term
u(x).' The paper gives an algorithm for the construction.of a
uniform approximation to the function'Pz(s). This algorithm is
based on the following principle of regularity: for any a, the
lamily za(s) belongs to a compact class containing z(s); u
CL(x)
tends to u(x) as a tends to zero. The functional
Card 1/2

L 14363-63
ACCESSION VR: AP3003840
M'y 1z(s)j tr(x)l NNW, 1M(X)3 + antz(s)]
yields the principal results given c>O, there exists a 6>0 such
that, corresponding to u*(x), with 1ju*(x) - u(x)11 0 (3)
A.Card /2.

L 4292-66-
]ACCESSION NRt AP5024202
the unverifiable restriction of independence of the rows of A. He con-
istructs an example in which arbitrarily small input changes lead to large output
changes (changes of the minimum of Cl which may lead to nonuniqueness). He gives
sufficient conditions for uniqueness and proves existence, giving an algorithm for
obtaining a solution of (1) stable with respect to small. perturbations of input
data A, ill and C# Orig. arto has! 3 formulas,
IASSOCIATION: none
~SUBMITTED- 2OApr64 ENCLt 00 SUB CODE: MA
:;NO REF.SOVt -004 am, 001
Card '2

TIKHOIMVP A.N. (Moskva)
ystems.
Stability of algorithms for the sclution of degenerate T
of linear algebraic equations. Zhur. vych. mat. I mat. fiz.
5 no.4%718-722 JI-Ag 165. (MIRA 18:8)

TIKHONOV, -Akl,,_BAKIlVAIOV, N.S.
........ -- - - ,
AU-Union Conference on Computer Mathematics. Zhur. -rich.
mat, i mat, fiz. 5 no.4:779-780 JI-Ag 165s (MIRA 18;8)

L 2283-66 51T(m)/EFF (n) -211WA (h) DY
'::ACCESSION NR: AP5016927 UM0089/65/018/006/0588/05931'
621.039-519.22
~AUTHORS: Tikhonov, A. N.; Arsenin, V. Ya.; Dumova, A. N.; Mayorov
i -
L. V. ; -r39TU76T',--
'TITLE: New method of reconstruction of true spectra
!SOURCE: Atomnaya energiya, v. 18, no. 6, 1965, 588-593
ITOPIC TAGS, neutron spectrum, neutron energy distribution, nuclear
Ireactor ob;racteristic, integral equation, Fredholm equation
ABSTRACT: The article presents two examples of the use of a new
method of solving problems based on ineomplete experimental data,
which arise in the reduction of results of experiments on nuclear re-
actors. This method was developed by one of the authors (Tikhonov,
DAN SSSR v. 149, 529, 1963) for Fredholm equations of the first kind.
The first example considers the reconstruction of the true energy
.spectrum of' e2ithermal neutronslin a uranium block of a reactor from
~tbe results of weasuremen with the aid of a mechanical selector.
Card 1/2

L 2283-66
ACCESSION NR: AP5016927
IThe second example id devoted to the calculation of the scalar energy
!flux. of thermal neutrons In a heterogeneous lattice moderator, from
imeasuz,ements of the directional flux. The examples illustrate the
)possibility of solving some problems in reactor physics in which the
I
iexperimentally obtained spectra are distorted because of shortcomings
lof the measurement apparatus or of the me thod. Orig. art. has: 4
1 figui4es and 9 formulas
IASSOCIATION: None
I
iSUBMITTED: 15Jun64 ENCL: 00 SUB CODE: NP
i
jNR REFSOV: 004 OTHER: 003
Card
2/? J') to

t AN c'SSR.

ACC NR: AT6035242 SOURCE CODE: UR/3043/66/000/005/601M,320
AUTHOR: -ikhonov,.A. N.; Gorbunov, A. D.; Gaysarryan, S. S.
. t--' -
ORG: none
TITLE: Description of an algorithm for optimun mesh construction in solvinZ the
Cauchy problem for ordinary differential equations by Runge Kutta methods
SOURCE: 'Moscow. Universitet. Vychislitel'nyy tsentr. Sbornik rabot, no. 5, 1966.
Vychislitel'nyye metody i programmirovaniye (Computing methods and programming), 17-20
oblem, Runge Ku-6ta
TOKC TAGS: Cauchy pr ,,,method, ordinary differential equation,
algorithm, differential equation solution
ABSTR-kCT: A method is proposed for selecting optimum inhomogeneous meshes when numer,7'
ically solving a system of N ordinary differential equations:
Y, f (x- Y) Y (xo) = !/0
(Y and fare N-dimensional vectors) in the xo 4 x 4 R segment by a Runge-Kutta method;
of degree s. Mesh optimality denotes that at point R the prescribed accuracy c is
obtained in the least possible number of steps. An inhomogeneous mesh (network) is
given by means of constantX , termed the parameter of the network, and the continuous-~-
ly differentiated function ~(x) of the distribution of the network steps so that at
any node xi (-(x0, x) integration step hi is determined by
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ACC NR: A-16035242
Optimality of the network is achieved by proper selection of netwo'rk7parameterX and
kunct ion ~W. The algorithm in question is for the solution of eq. (1) and embodies!
a preliminary computation which, although:it does not give y(R) with the necessar,
y
accuracy, still makes it possible to compute Xand gx), which makes it possible to
achieve the required accuracy at point R on the second calculation. The paper gives
a method for solving Eq. (1) when N - 1, and adduces two examples of Cauchy problems
solved. Orig. art. has: 10 formulas.
SUB CODE: 12/.' SUBM DATE: none/ ORIG REF: 001/ OTH REF: 001
2/2

A11C N1,
AP6025919
AUTHOR: Tikhonov, A. N. (Moscow)
ORG:
SOURCE CODE: UR/0208/66/006/004/0631/0634'
none
TITLE: On stability of the problem of optimizing'functionals
SOURCE: Zhurnal vychislitel'noy matematiki i matematic'heskoy fiziki, v. 6, no. 4,
631-634
TOPTC TAGS: function analysis, optimization, mathematic space
ABSTRACT: The problem of finding an element which minimizes a given functional has
attracted and undoubtedly will continue to attract increasingly greater interest in
applied mathematics. Given functional F(z) in some metric space Z, let the problem
of minimizing F(z) in Z have a unique solution, i.e., let there be a zo which is the
sole element of Z in-which F(z) reaches its minimnm F(zO) = F