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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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

## 电子工程代写|并行计算代写Parallel Computing代考|Fixed Point Formats

The simplest scheme one might come up with for a machine is a fixèd point storage format. In fixed point notation, we write down all numbers with a certain number of digits before the decimal point and a certain number after the decimal point. With four digits (decimal) and two leading digits, we can, for example, write the number three as 0300 . This means 03.00. Fixed point storage is the first variant I have sketched in our introductory thought experiment.

We immediately see that such a representation is not a fit for scientific computing. Let $x=3$ in the representation be divided by three. The result $x / 3=1.00$ suits our data structure. However, once we divide by three once more, we start to run into serious trouble. Indeed $1 / 3 \approx 0.33$-which is the closest value to $1 / 3$ we can numerically encode-is already off the real result by $0.00 \overline{3}$.

You might be tempted to accept that you have a large error. But as a computational scientist, you neither can accept that most of your bits soon start to hold zeroes, i.e. no information at all, nor that your storage format is only suited to hold numbers from a very limited range (basically from $0.01$ to 30 and even here with quite some error).

## 电子工程代写|并行计算代写Parallel Computing代考|Decimal versus binary notation

On the next pages, we use two types of number presentations: decimal and binary. Decimal is what we use in everyday life. We write down numbers like $a_{1} a_{2} a_{3} a_{4} \cdot a_{5} a_{6} a_{7} \cdot 10^{a_{8} a_{9}}$, where $a_{i} \in{0,1, \ldots, 9}$. Technically, this means that we write down numbers as $\left(a_{4} \cdot 10^{0}+a_{3} \cdot 10^{1}+a_{2} \cdot 10^{2}+a_{1} \cdot 10^{3}+a_{5} \cdot 10^{-1}+\right.$ $\left.a_{6} \cdot 10^{-2}+a_{6} \cdot 10^{-3}\right) \cdot 10^{a_{9} \cdot 10^{0}+a_{8} \cdot 10^{1}}$. Note how we work our way through the digits starting from the decimal point both towards the left and the right, but also for the exponent $\left(a_{8}\right.$ and $a_{9}$ ). If I want to make it very clear that we are using this decimal system, I attach $\left.\right|_{10}$ to the numbers. If nothing is written down, you may assume that any number is given for a base of 10 .

On a computer, a different data representation is used: a binary system. Here, the digit sequence $a_{1} a_{2} a_{3} a_{4} \cdot a_{5} a_{6} a_{7}$ has a different meaning. First, we use a base of 2 for the scaling of the entries. Second, the $a_{i}$ s are from ${0,1}$ only. Third, we would use $2^{a_{8} a_{9}}$ if we had a scientific notation. In a binary system, digit sequences denote the number $\left(a_{4} \cdot 2^{0}+a_{3} \cdot 2^{1}+a_{2} \cdot 2^{2}+a_{1} \cdot 2^{3}+a_{5} \cdot 2^{-1}+a_{6} \cdot 2^{-2}+a_{7} \cdot 2^{-3}\right)$. If required, I will write $\left.a_{1} a_{2} a_{3} a_{4} \cdot a_{5} a_{6} a_{7} \cdot 2^{a_{8} a_{9}}\right|_{2}$ to make it clear that I’m using a binary base.

We conclude that we search for a scheme where the number of positions after the deccimal point is not fixed. This way, wé can cover a way bigger vâlue range than with fixed point formats. We are more flexible. At the same time, the new format should run as efficient as possible on our hardware and its memory footprint should be under control. It should work with a fixed, predetermined number of bytes. In computer architecture, there used to be a zoo of such formats.

# 并行计算代考

## 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。

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