### 数学代写|数值分析代写numerical analysis代考|CIVL5458

statistics-lab™ 为您的留学生涯保驾护航 在代写数值分析numerical analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数值分析numerical analysis代写方面经验极为丰富，各种代写数值分析numerical analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|数值分析代写numerical analysis代考|COMPUTATIONAL METHODS FOR ERROR

This chapter is intended to make the student aware of the possible sources of error and to point out some techniques which can be used to avoid these errors. In appraising computer results, such errors must be taken into account. Realistic estimates of the total error are difficult to make in a practical problem. and an adequate mathematical theory is still lacking. An appealing idea is to make use of the computer itself to provide us with such estimates. Various methods of this type have been proposed. We shall discuss briefly five of them. The simplest method makes use of double precision. Here one simply solves the same problem twice-once in single precision and once in double precision. From the difference in the results an estimate of the total round-off error can then be obtained (assuming that all other errors are less significant). It can then be assumed that the same accumulation of roundoff will occur in other problems solved with the same subroutine. This method is extremely costly in machine time since double-precision arithmetic increases computer time by a factor of 8 on some machines, and in addition, it is not always possible to isolate other errors.

A second method is interval arithmetic. Here each number is represented by two machine numbers, the maximum and the minimum values that it might have. Whenever an operation is performed, one computes its maximum and minimum values. Essentially, then, one will obtain two solutions at every step, the true solution necessarily being contained within the range determined by the maximum and minimum values. This method requires more than twice the amount of computer time and about twice the storage of a standard run. Moreover, the usual assumption that the true solution lies about midway within the range is not, in general, valid. Thus the range might be so large that any estimate of the round-off error based upon this would be grossly exaggerated.

A third approach is significant-digit arithmetic. As pointed out earlier, whenever two nearly equal machine numbers are subtracted, there is a danger that some significant digits will be lost. In significant-digit arithmetic an attempt is made to keep track of digits so lost. In one version only the significant digits in any number are retained, all others being discarded. At the end of a computation we will thus be assured that all digits retained are significant. The main objection to this method is that some information is lost whenever digits are discarded, and that the results obtained are likely to be much too conservative. Experimentation with this technique is still going on, although the experience to date is not too promising.

## 数学代写|数值分析代写numerical analysis代考|SOME MATHEMATICAL PRELIMINARIES

It is assumed that the student is familiar with the topics normally covered in the undergraduate analytic geometry and calculus sequence. These include elementary notions of real and complex number systems; continuity; the concept of limits, sequences, and series; differentiation and integration. For Chap. 4, some knowledge of determinants is assumed. For Chaps. 8 and 9, some familiarity with the solution of ordinary differential equations is also assumed, although these chapters may be omitted.
In particular, we shall make frequent use of the following theorems.
Theorem 1.1: Intermediate-value theorem for continuous functions Let $f(x)$ be a continuous function on the interval $[a, b]$. If $f(x) \leq \alpha \leq f(\bar{x})$ for some number a and some $x, \bar{x} \in[a, b]$, then
$$\alpha=f(\xi) \quad \text { for some } \xi \in[a, b]$$
This theorem is often used in the following form:
Theorem 1.2 Let $f(x)$ be a continuous function on $[a, b]$, let $x_l, \ldots, x_n$ be points in $[a, b]$, and let $g_l, \ldots, g_n$, be real numbers all of one sign. Then
$$\sum_{i=1}^n f\left(x_i\right) g_i=f(\xi) \sum_{i=1}^n g_i \quad \text { for some } \xi \in[a, b]$$

# 数值分析代考

## 有限元方法代写

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## 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。