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[[Category:Numerical analysis and scientific computing]]

...therwise it is called defective. The notion is of particular importance in numerical [[Linear-algebra(2)|linear algebra]]. A complex matrix $A$ is non-defective if and only if it is [[Similar matrices|similar]] to a [[diagonal matrix]]: $\Delt

...sed in percentages. The smallest possible numbers are taken as $\Delta(a)$ and $\delta(a)$. ...ent) and the frequencies of different values of the difference between $x$ and $a$. Probabilistic methods are used in the last approach (see [[Errors, the

...nds there are one-placed (unary or monadic), two-placed (binary or dyadic) and many-placed (or polyadic) operations. In distinguishing between the position of the operand and the operand as an actual argument, the concept of transforming or coercing

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...ation step is satisfactory. Now replace the initial point $x_0$ by $x_0+h$ and repeat the entire procedure. This yields an approximate solution $y^2$; the ...rmula for $y^2$, the method described here for the estimation of the error and the selection of the integration step is known as an imbedded Runge–Kutta

$#C+1 = 31 : ~/encyclopedia/old_files/data/I052/I.0502080 Interval analysis Please remove this comment and the {{TEX|auto}} line below,

...oice of these parameters. The optimization problem can take various forms, and may reduce, for example, to a transition from a method of simple iteration, ...matrix $L$ and can be fairly slow for large $\nu(L)$. In such situations, and particularly for the solution of systems of grid equations, modifications o

...after one elementary step the value of the quadratic form is only reduced and not minimized, the relaxation method is called an incomplete relaxation met ...er relaxation, where the matrix $A$ possesses the so-called property $(A)$ and is ordered accordingly. A matrix $A$ is called a matrix possessing property

Please remove this comment and the {{TEX|auto}} line below, ...ge [[#References|[1]]] and developed later by W. Kutta [[#References|[2]]] and others. Originally, this idea was used only for constructing explicit schem

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...e model, and analyzing the results for stability, speed of implementation, and appropriateness to the situation. ...ne of numerical analysis involves the design of techniques that take these and other error-producing situations into account when approximating the soluti

...all png images have been replaced by TeX code, please remove this message and the {{TEX|semi-auto}} category. A numerical technique proposed in 1960 by P.D. Lax and B. Wendroff [[#References|[a6]]] for solving, approximately, systems of hyp

If the TeX and formula formatting is correct, please remove this message and the {{TEX|semi-auto}} category. An iterative optimization procedure [[#References|[a4]]] for computing

...uthor(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike Lic Department of Computing and Mathematics, University of Derby,

Please remove this comment and the {{TEX|auto}} line below, ...son with classical (analytical) mathematical methods, considerably broader and encompasses practically all sciences. In the simplest case, a cybernetic sy

...uter; the automatic execution of user jobs into the computer is organized; and effective use of the computer equipment is provided (see [[#References|[1]] ...of view of being able to write algorithms, are very elementary operations, and writing down an algorithm (programming) as a sequence of these instructions

...formalizable was seen as "vague", "intuitive" (as opposed to "rigorous"), and imprecise.... This movement is later called 'the discretization program'".< ...the arithmetization program signified efforts to develop a foundation for analysis, i.e. the calculus, in terms of the natural numbers