The left elimination method. The counter elimination method. Still using the framework of the right elimination method (formulae (10)-(15)) in reverse order, we obtain through such an analysis the computational formulae of the left elimination method [Pg.13]

The Gaussian elimination method provides a systematic approach for implementation of the described forward reduction and back substitution processes for large systems of algebraic equations. [Pg.200]

Stability of the elimination method. Let us stress that the conditions (7i — a yf 0 and 1 — Q cannot be excluded or relaxed during the [Pg.11]

Of course, the counter elimination method could be especially effective in an attempt to determine yi merely at only one node i = i. [Pg.14]

Returning to the right elimination method, we show that the conditions ai < 1 guarantee that the error 6yi y = — j/j+i arising when [Pg.12]

SOLUTION ALGORITHMS GAUSSIAN ELIMINATION METHOD 205 6.4.2 Frontal solution technique [Pg.205]

Joint use of the left and right elimination methods refers to the counter elimination method. The essence of this method is to consider a fixed inner [Pg.13]

Formulae (74)-(75) show that the elimination method is stable. The values and should be known before proceeding to the applications of (70), (74) and (75). For this reason we involve here the second boundary condition (67) and relation (69) for i = N [Pg.36]

The computational formulae of the right elimination method help derive estimate (38) [Pg.22]

SOLUTION ALGORITHMS BASED ON THE GAUSSIAN ELIMINATION METHOD [Pg.203]

To describe the basic concept of the Gaussian elimination method we consider the following system of simultaneous algebraic equations [Pg.200]

We give below without proving the algorithm of the cyclic elimination method which will be used in the sequel [Pg.38]

These equations admit the form (39) and can be solved by the elimination method. The main difference from the cylindrical case lies in the selection rules for and d. To obtain the formulae for

[Pg.197]

The most frequently used modifications of the basic Gaussian elimination method in finite element analysis are the LU decomposition and frontal solution techniques. [Pg.203]

Solution estimation for difference bormdary-value problems by the elimination method. In tackling the first boundary-value problem difference equation (21) has the tridiagonal matrix of order TV — 1 [Pg.21]

With the aid of effective Gauss method for solving linear equations with such matrices a direct method known as the elimination method has been designed and unveils its potential in solving difference equations, [Pg.9]

The algorithm presented below as the sequence of applied formulae is called the right elimination method and is showing the gateway for the [Pg.10]

This result is remarkably simple as compared to the usual methods. For a spin-polarised potential V, Kraft, Oppeneer, Antonov and Eschrig (1995) used the elimination method and found the corrections as a sum of 9 terms, which is equivalent to our Eq.(ll). They notice that three terms of their sum have a known physical meaning (spin-orbit, Darwin and mass-velocity corrections), but the other terms have no special name . [Pg.454]

Thus emerged the system of algebraic equations with a tridiagonal matrix. Because of this form, the elimination method may be useful (see Chapter 1, Section 1). [Pg.75]

The most important direct solution algorithms used in finite element computations are based on the Gaussian elimination method. [Pg.200]

The natural replacement of the central difference derivative u x) by the first derivative Uo leads to a scheme of second-order approximation. Such a scheme is monotone only for sufficiently small grid steps. Moreover, the elimination method can be applied only for sufficiently small h under the restriction h r x) < 2k x). If u is approximated by one-sided difference derivatives (the right one for r > 0 and the left one % for r < 0), we obtain a monotone scheme for which the maximum principle is certainly true for any step h, but it is of first-order approximation. This is unacceptable for us. [Pg.184]

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