''in the numerical solution of algebraic equations''
...numerical methods of linear algebra is the scheme of inverse (or backward) analysis. Applied to the solution of linear algebraic equations
18 KB (2,636 words) - 08:00, 13 May 2022
...[a1]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)</TD></TR></table>
3 KB (407 words) - 12:57, 19 December 2020
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> V.V. Voevodin, "Numerical methods of algebra. Theory and algorithms" , Moscow (1966) (In Russian)</
...>[a7]</TD> <TD valign="top"> A.S. Householder, "Principles of numerical analysis" , McGraw-Hill (1953)</TD></TR></table>
10 KB (1,498 words) - 08:08, 21 March 2022
...op"> W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, "Numerical recipes" , Cambridge Univ. Press (1986) pp. §9.2</TD></TR></table>
5 KB (766 words) - 08:12, 6 June 2020
Methods for obtaining analytical expressions (formulas) or numerical values which approximate to some degree of accuracy the required particular
...employed in theoretical investigations and are used only rarely to obtain numerical solutions of differential equations in practical computations.
32 KB (4,604 words) - 16:55, 7 February 2011
The use of the Euler–MacLaurin sum formula in numerical [[Quadrature|quadrature]] is discussed in [[#References|[a1]]] and [[#Refer
...[a1]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="
5 KB (745 words) - 09:18, 6 January 2024
$#C+1 = 187 : ~/encyclopedia/old_files/data/F041/F.0401430 Fredholm equation, numerical methods
...the second kind one uses the language of [[Functional analysis|functional analysis]]. The integral equation (1) can be written as a linear operator equation
20 KB (3,019 words) - 03:31, 14 June 2022
...theory (cf. [[Transport equations, numerical methods|Transport equations, numerical methods]]), plasma physics, including the inverse problems for these most i
...n of the conditions for the appearance of new physical effects, etc. Thus, numerical experiments usually expand the domain of effective utilization of mathemati
13 KB (1,857 words) - 21:26, 8 November 2014
...> <TD valign="top"> J. Stoer, R. Bulirsch, "Introduction to numerical analysis" , Springer (1980) pp. 285–287</TD></TR><TR><TD valign="top">[a2]</TD>
13 KB (1,768 words) - 17:09, 7 February 2011
A second approach to the plan of analysis of stability and convergence dispenses with the need to consider fractional
...for some nonstationary problems" J. Miller (ed.) , ''Topics in numerical analysis'' , Acad. Press (1973) pp. 63–87 (Translated from Russian)</TD></TR><T
12 KB (1,750 words) - 11:54, 26 March 2023
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
5 KB (756 words) - 18:15, 25 June 2020
...nstructed by specialists in the area concerned with the problem. Numerical analysis is concerned with devising methods for approximating the solution to the mo
...n lead to significant errors in approximation. The discipline of numerical analysis involves the design of techniques that take these and other error-producing
29 KB (4,373 words) - 17:21, 2 January 2021
...ust solve a linear boundary value problem, which makes it necessary to use numerical methods and some discretization of the original problem and the linear prob
...chultz, A.H. Sherman, "The application of sparse matrix methods to the numerical solution of nonlinear elliptic partial differential equations" D.L. Colton
9 KB (1,320 words) - 22:17, 5 June 2020
...es|[a7]]] for methods for calculating exact values of the discrepancy. The numerical values differ only slightly from the upper bound in (a8).
...d exactly, since the points $P _ { k }$ are again points of a lattice. The numerical values show that a sequence of type (a9) behaves as good in dimension $k \t
11 KB (1,696 words) - 19:30, 8 February 2024
...that can be solved on computers is high, being determined by the amount of numerical information needed to specify the matrix.
...gn="top">[4]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
9 KB (1,376 words) - 17:46, 4 June 2020
...ssence, the first part of the question is a basic problem of the theory of numerical methods and in most cases it is studied independently of the optimization p
In the practice of numerical integration, active algorithms of the type of integration algorithms with a
12 KB (1,798 words) - 20:07, 12 January 2024
...blem|Stefan problem]], or the phase-transition problem. The most effective numerical method for solving these problems is the calculus of finite differences, wh
...ion between the field of temperatures and other physical phenomena. In the analysis of problems involving the freezing of soil with allowance for the inflow of
4 KB (563 words) - 07:56, 15 July 2014
...sion of the problem increases, the number of operations needed to obtain a numerical solution increases correspondingly, both on account of the larger number of
...dent partial differential equations" , ''The state-of-the-art in numerical analysis. Proc. Conf. Univ. York, 1976'' , Acad. Press (1977) pp. 757–796</TD></
6 KB (763 words) - 19:39, 5 June 2020
One of the notions in [[Non-linear functional analysis|non-linear functional analysis]].
...E$. An operator $A$ is called semi-continuous if for any $u,v,w\in E$ the numerical function $(A(u+tv),w)$ is continuous in $t$. An example of a semi-continuou
4 KB (605 words) - 17:10, 14 February 2020
...atrix|inverse matrix]]. As for the solution of linear systems, methods for numerical inversion can be subdivided into direct and iterative methods; however, ite
...ate inverse matrix. This is an important difference between the problem of numerical inversion of a matrix and the solution of linear systems, where (for exampl
11 KB (1,584 words) - 22:13, 5 June 2020