...cumulated errors in larger calculations. Analysis of accumulated errors in numerical methods permits one to describe methods according to their susceptibility t
...gn="top">[3]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
3 KB (515 words) - 18:22, 18 April 2023
...a particular case of the [[Adjustment method|adjustment method]]. For the numerical solution of (1), or (2), one may, use, e.g., difference methods. In depende
...</TR><TR><TD valign="top">[3]</TD> <TD valign="top"> Yu.G. Evtushenko, "Numerical optimization techniques" , Optim. Software (1985) (Translated from Russia
4 KB (519 words) - 22:10, 5 June 2020
...n="top">[a3]</TD> <TD valign="top"> B. Wendroff, "Theoretical numerical analysis" , Acad. Press (1966) pp. Chapt. 1</TD></TR></table>
3 KB (522 words) - 20:12, 10 January 2024
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
1,010 bytes (152 words) - 08:54, 25 November 2018
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...> <TD valign="top"> Maurice V. Wilkes, "A short introduction to numerical analysis", Cambridge University Press (1966) {{ISBN|0-521-09412-7}} {{ZBL|0149.10902
4 KB (592 words) - 08:09, 26 November 2023
...is [[Degenerate_matrix|singular]] then $\kappa(A)=\infty$. In [[numerical analysis]] the condition number of a matrix $A$ is a way of describing how well or b
974 bytes (157 words) - 19:31, 15 December 2020
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...[a2]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , Addison-Wesley (1956)</TD></TR></table>
4 KB (533 words) - 10:58, 29 May 2020
...)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> G.N. Lance, "Numerical methods for high speed computers" , Iliffe (1960)</TD></TR></table>
...e) solution $y^1$ is three. Hence, in general, the difference of these two numerical approximations is only of order three, so that a conservative error estimat
7 KB (1,053 words) - 17:13, 14 February 2020
...use of electronic computers made it necessary to impose new conditions on numerical methods; the main problem at that stage was to develop new, "computer-frie
...arious fields of scientific and everyday activity, and may be described as analysis of mathematical models. The second is the development of methods and algori
13 KB (1,892 words) - 20:11, 31 December 2018
...[a3]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)</TD></TR></table>
3 KB (505 words) - 14:56, 14 February 2020
...opedia/old_files/data/N067/N.0607080 Non\AAhlinear boundary value problem, numerical methods
...roblems for systems of ordinary differential equations, the description of numerical methods usually proceeds without indication of a discretization of the orig
19 KB (2,657 words) - 14:54, 7 June 2020
A method for approximating an [[integral operator]] by constructing numerical methods for the solution of integral equations. The simplest version of a q
...align="top"> L.V. Kantorovich, V.I. Krylov, "Approximate methods of higher analysis" , Noordhoff (1958) (Translated from Russian) {{MR|0106537}} {{ZBL|0083.353
2 KB (335 words) - 16:32, 13 July 2021
...dmund Whittaker, G. Robinson, "The calculus of observations. A treatise on numerical mathematics" (4th ed.) Blackie & Son (1954) p.99. {{ZBL|0058.33603}}</TD></
...<TR><TD valign="top">[a2]</TD> <TD valign="top"> A.S. Householder, "The numerical treatment of a single nonlinear equation" , McGraw-Hill (1970)</TD></TR></
3 KB (496 words) - 09:54, 29 May 2020
...ds of gas dynamics (cf. [[Gas dynamics, numerical methods of|Gas dynamics, numerical methods of]]), there are 6 different forms of viscosity matrices (see [[#Re
...ference schemes (see [[#References|[10]]]), it is possible, by varying the numerical values of the parameters, to change the values of the terms of the viscosit
7 KB (987 words) - 14:03, 24 December 2020
$#C+1 = 31 : ~/encyclopedia/old_files/data/I052/I.0502080 Interval analysis
A theory intended for the calculation of rounding errors of calculations on numerical computers. Since not all numbers can be represented exactly in a computer w
5 KB (677 words) - 22:13, 5 June 2020
[[Category:Numerical analysis and scientific computing]]
1 KB (217 words) - 18:54, 19 October 2014
...tandard procedure is usually applied to the use of mathematical methods in numerical calculations on a computer (computational mathematics, mathematical statist
...]</TD> <TD valign="top"> V.V. Voevodin, O.B. Arushanyan, , ''Numerical Analysis in FORTRAN'' , Moscow (1979) pp. 73–84</TD></TR><TR><TD valign="top">[2
3 KB (372 words) - 17:12, 7 February 2011
...htarrow \mathbf{C} ^ { n }$, is concerned with the question of whether the numerical discretization inherits the dynamic properties of the differential equation
...solutions is a non-increasing function of $x$. Let $y_1$, $z_1$ denote the numerical solutions after one step of size $h$ with initial values $y _ { 0 }$, $z_0$
9 KB (1,275 words) - 17:43, 1 July 2020
...s for the numerical integration (cf. [[Integration, numerical|Integration, numerical]]) of diffusion problems, introduced by J. Crank and P. Nicolson [[#Referen
and numerical initial condition
14 KB (2,138 words) - 08:45, 28 January 2024
are the numerical parameters of the method. If $ \epsilon ^ {k} = u - u ^ {k} $,
...tor equations, and polynomials deviating least from zero" , ''Mathematical analysis and related problems in mathematics'' , Novosibirsk (1978) pp. 89–108
16 KB (2,300 words) - 19:29, 17 January 2024