...gn="top">[5]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...[a4]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , Dover, reprint (1987) pp. Chapt. 8 {{MR|0895822}} {{ZBL|0641.65001}}
4 KB (605 words) - 08:02, 6 June 2020
...e form (2), (3) are already implicit. This complicates significantly their numerical implementation: The values $ k _ {n} $,
The approaches to the construction of numerical methods considered above for equations of type (1) can be extended to ordin
9 KB (1,315 words) - 20:04, 15 January 2024
...ign="top"|{{Ref|Ba}}||valign="top"| N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations", MIR (1977) (Translated from R
...{Ref|KaAk}}||valign="top"| L.V. Kantorovich, G.P. Akilov, "Functional analysis", Pergamon (1982) (Translated from Russian) {{MR|0664597}} {{ZBL|0484.4
3 KB (519 words) - 19:10, 6 April 2012
...d in some way with the existence of an invariant structure (see [[Harmonic analysis, abstract]]), when they are eigen functions of the [[Laplace–Beltrami equ
...ory (see [[#References|[6]]] and [[#References|[7]]]) and in the theory of numerical integration (see [[#References|[8]]]).
4 KB (575 words) - 20:24, 20 December 2016
$#C+1 = 73 : ~/encyclopedia/old_files/data/I051/I.0501430 Integral equations, numerical methods
is a numerical parameter and $ K ( x , s ) $
12 KB (1,747 words) - 13:26, 14 January 2022
...op"> W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, "Numerical recipes" , Cambridge Univ. Press (1986) pp. 105ff</TD></TR>
3 KB (476 words) - 16:30, 29 March 2024
...attice points are also of importance in crystallography, coding, numerical analysis, analytic number theory, Diophantine approximation, computational geometry,
2 KB (239 words) - 19:03, 2 October 2016
...[a2]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)</TD></TR></table>
3 KB (490 words) - 17:39, 14 December 2020
|valign="top"|{{Ref|Ba}}||valign="top"| N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
1 KB (234 words) - 21:21, 15 July 2012
...</TD> <TD valign="top"> N.S. Bakhvalov, "On an estimate of the error at numerical integration of differential equations by Adams' extrapolation method" ''Do
...d-held programmable calculator" G.H. Golub (ed.) , ''Studies in numerical analysis'' , Math. Assoc. Amer. (1984) pp. 199–242</TD></TR></table>
6 KB (888 words) - 21:01, 4 April 2020
...clopedia/old_files/data/E035/E.0305170 Eigen values of integral operators, numerical methods
Numerical methods for computing the complete spectrum of an integral operator or a pa
11 KB (1,669 words) - 19:37, 5 June 2020
$#C+1 = 29 : ~/encyclopedia/old_files/data/W097/W.0907160 Wavelet analysis
In wavelet analysis scaled and displaced copies of the basic wavelet $ g $
6 KB (909 words) - 08:28, 6 June 2020
...rithms. Many problems suffer from the curse of dimension. Examples include numerical integration, optimal recovery (approximation) of functions, global optimiza
...average-case setting (see [[Bayesian numerical analysis|Bayesian numerical analysis]]).
12 KB (1,706 words) - 20:29, 9 December 2023
...ology "best formula" is often encountered in the literature on numerical analysis, but, as was observed in [[#References|[a2]]], p. 75, it should be taken wi
...)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> H. Engels, "Numerical quadrature and cubature" , Acad. Press (1980)</TD></TR></table>
4 KB (658 words) - 10:58, 29 May 2020
...ign="top">[1]</TD> <TD valign="top"> S.L. Sobolev, "Some remarks on the numerical solution of integral equations" ''Izv. Akad. Nauk SSSR Ser. Mat.'' , '''20
...gn="top">[4]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
4 KB (651 words) - 17:23, 14 February 2020
...10/b1100108.png" />) are of no use for an appropriate characterization and
analysis of methods which are able to efficiently integrate a stiff problem. Thus th
...a coefficients entailing B-stability was derived ( "algebraic stability in
numerical analysisalgebraic stability" ). The notion of <img align="absmiddle" border
11 KB (1,517 words) - 17:23, 7 February 2011
...lign="top">[4]</TD> <TD valign="top"> A.A. Samarskii, E.S. Nikolaev, "Numerical methods for grid equations" , '''1–2''' , Birkhäuser (1989) (Translate
.../TD> <TD valign="top"> U.M. Ascher, R.M.M. Mattheij, R.D. Russell, "Numerical solution for boundary value problems for ordinary differential equations" ,
7 KB (1,036 words) - 19:36, 5 June 2020
...solved, this system has the form of a recurrence relation here. For other numerical methods, see [[#References|[a1]]]. Volterra equations of the first kind are
...<TD valign="top"> A.E. Taylor, D.C. Lay, "Introduction to functional analysis" , Wiley (1980)</TD></TR></table>
13 KB (1,966 words) - 08:28, 6 June 2020
A very simple finite-difference method for the numerical solution of an ordinary differential equation. Let a differential equation
The numerical algorithm of the Euler method can easily be programmed on a computer.
6 KB (877 words) - 19:38, 5 June 2020
...see [[Multi-dimensional statistical analysis|Multi-dimensional statistical analysis]]). If the results of observations $ X _ {1} \dots X _ {n} $
degrees of freedom. This fact forms the basis of the [[Hotelling test]]. For numerical calculations one uses tables of the [[Beta-distribution|beta-distribution]]
4 KB (517 words) - 19:08, 26 May 2024