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# 数学代写|优化理论代写Optimization Theory代考|CS586/IE519 Elements of the Computing Theory

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## 数学代写|优化理论代写Optimization Theory代考|Elements of the Computing Theory

Since every year the complexity of scientific and applied problems is increasing, there is an uprise of the need of a large amount of process of input data with the use of computing machinery for the numerical computation, and optimization of computations by all rational methods and means is a topical and important question. As a rule, the solution of the applied problems reduces to solving the typical problems of computational mathematics. Computational mathematics is a science about the methods of numerical solving problems of applied mathematics using modern computing machinery. The subject of computational mathematics is numerical methods $(\mathrm{NM})$ or, that is the same thing, the multitude of computational algorithms (CA) and the question of their substantiation: the convergence and speed of $\mathrm{NM}$ convergence, their stability and error, the optimality on different criterion, the implementation time on the computing machinery, the necessary memory of computing machinery, etc.

The purpose of this chapter is to explain the main concepts and some results of computational mathematics, which are repeatedly used in the monograph, and at the same time, they have an independent value. The presentation of this information, in our opinion, is necessary for a confident possession of the given material.
In the first chapter:

• Certain supporting data in the theory of computing is given for determining the accuracy of the approximate solving problem, the quality of the used algorithm, and the comparative study of various algorithms according to some criteria.
• The principal features of the CA are determined (accuracy, execution time, necessary memory of the computing machinery), and the methods of their estimate are provided.
• There is a definition of optimal (inaccuracy and high speed), asymptotically optimal, and optimal in the order algorithms.
• The questions of identifying and clarifying a priori information on the problem are considered in cases when a priori information is not incorrectly set in the order to improve the quality of the obtained approximate solutions of a problem.

## 数学代写|优化理论代写Optimization Theory代考|Theory of Error Computations

One of the main directions of development of modern computational mathematics is the improvement of the theory of error computations, the research of comparative study of $\mathrm{CA}$, and the optimal algorithm development in the solving problems of computational and applied mathematics.

The solution of the majority of the problems with modern computing tools is based on the computational experiment (CE), which seamlessly unites the mathematical model (MM), the computational algorithm (CA), the computations on the computing machinery, and the experiment. CE is necessary for obtaining an adequate quantitative description of the studied phenomenon or process itself with the necessary accuracy for the least possible machine time. The process of observations and comparing them with the matched model of $\mathrm{MM}$ is conducted on the computing machinery to check the validity of MM. The implementation of MM is performed with the use of numerical methods (NM), which approximate the input model and make it suitable for practical use. The errors of this approximation, as well as the rounding errors in the implementation of $\mathrm{NM}$ on the computing machinery and the errors of measurement or observation of implementation of the studied process, must be considered in determining errors of $\mathrm{MM}$ or the adequacy of $\mathrm{MM}$ and in the process itself. The errors of input MM must be considered in the process of definition of the requirements for the accuracy of the solution of various problems that are solved within this model.

In this monograph, the most important computational aspects of the determination of the error of MM and constructing its optimal implementation are analyzed. The multifaceted approach is based on the analysis of the three main characteristics of the corresponding NM-accuracy, implementation time, and necessary memory on computing machinery. According to these characteristics, the comparative study and the optimization of the corresponding $\mathrm{NM}$ are performed.

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。