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# 数学代写|优化理论代写Optimization Theory代考|MA208 Classification of Problems and Creation of Testing Sets

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## 数学代写|优化理论代写Optimization Theory代考|Classification of Problems and Creation of Testing Sets

The systematization of classes of problems of computational mathematics is given on the most general functional features (see p. 1.1) in [267]. It is also noted that further systematization of problems should be performed within each class, emphasizing subclasses according to the given and used in NM by a priori information that relates to the structure, functional nature, properties and value of the input and output data of the problem, or other elements that generate this class. Such information will be called the as characteristics of problems in the future $[106,114,141,198]$. They can be both quantitative and qualitative.

The a priori data of qualitative and quantitative character are emphasized in the separate multitudes of $v=\left(v_1, \ldots, v_k\right)$ and $w=\left(w_1, \ldots, w_s\right)$, respectively. The presence of one or another information about the problem (from the sets of $v$ and $w$ ) allows to relate it to a certain class. Sets of a priori characteristics $v$ and $w$ can be replenished that leads to the constructing of new classes, the narrowing of existing ones. This approach of classification is given, for example, in [267]. So, a multitude $v$ can contain data about such properties of the operator and the elements of interest, such as continuity, smoothness, monotony, and convexity of the functions of interest. The elements of the multitude $w$ may be the accuracy of presenting and the amount of input information, the accuracy of solving problem, the constants that constrain the derivatives of the function of interest, etc. are required. New classes or “narrowing” of the output class may appear by means of additional a priori data. It should be noted that the more deep decomposition of classes of problem into more “narrow” subclasses are, in other words, the more characteristics $v_i$ and $w_j,(i=\overline{1, k}, j=\overline{1, s})$ will be the carriers of a specific information about the problem, the easier it will be to determine the sets of testing problems that reflect the properties of the problems of each subclass more fully; that means that the uncertainty of the conclusions of the test will be decreased.

## 数学代写|优化理论代写Optimization Theory代考|Conducting of a Computational Experiment

In mathematical terms, the computational experiment (CE) for the testing of CA programs can be written in the form of a relation:
$$U=A V$$
where $V=(I, X, C)$ is the set of input data; $A$ is CA program (mathematical operator or image); $U$ is a table of results.

The input data consists of a vector $I$ of input data of the problem from the domain of admissible values $D(I), I \in D(I)$, and fixed values of the controlling parameters $X$ from the range of admissible valuations $G(X), X \in G(X)$ where the CA-program is constructed, as well as by the constrained constants $C$ on the components of the choice $I$, parameters $X$ and stopping criterion. The vector $I$ dimension should coincide with the values of the controlling parameters $X$.

The result of $\mathrm{CE}$ is the information, the components of which is an approximate solution and data about the quality of the CA-program. This includes $E, T, M$ and (or) their estimates $\bar{E}, \bar{T}, \bar{M}$, the intervals of the differentiable behavior of the program on the characteristics of $E$ and $T$, data about other characteristics of the program, such as the coefficient of accuracy of the solution of testing problems, diagnostics of the functional behavior of the program for normal, extreme, and exceptional circumstances (situations) and other data that are individual for each program and for each testing problem. All these results should be summarized in the appropriate tables. These tables may vary in content and form depending from the program, class of problems and the testing objectives.

The valuations of the experimentally studied characteristics and programs $(E, T$, $M$ ) depend on the computing environment: the used computing machinery, operating system, translator, the mode of operation of the computering machinery (package, single program), the number of processors, etc. Therefore, to compare the results, it (environment) is predicted to be fixed.

## 数学代写|优化理论代写Optimization Theory代考|Classification of Problems and Creation of Testing Sets

[267] 中最普遍的功能特征 (参见第 1.1 页) 给出了计算数学问题类别的系统化。还应注意，应在每 个类中进一步系统化问题，根据与 NM 的输入和输出数据的结构、功能性质、属性和值相关的先验 信息，强调根据给定和在 NM 中使用的子类问题，或生成此类的其他元素。这些信息在末来将被称 为问题的特征 $[106,114,141,198]$. 它们既可以是定量的，也可以是定性的。

$w_j,(i=\overline{1, k}, j=\overline{1, s})$ 越是问题特定信息的载体，越容易确定更充分反映各子类问题属性的测试 问题集；这意味着测试结论的不确定性将降低。

## 数学代写|优伦理论代写Optimization Theory代考|Conducting of a Computational Experiment

$$U=A V$$

## MATLAB代写

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