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• 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

## 电气工程代写|数字信号过程代写digital signal process代考|Gaussian Elimination

A system of linear equations may be solved via an algorithm called Gauss elimination [5], shown in the computational flow below. We start by declaring a system of three equations $A X=B$.
$a_{11} x_1+a_{12} x_2+a_{13} x_3=b_1$
$a_{21} x_1+a_{22} x_2+a_{23} x_3=b_2$
$a_{31} x_1+a_{32} x_2+a_{33} x_3=b_3$
$\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33}\end{array}\right] \cdot\left[\begin{array}{l}x_1 \ x_2 \ x_3\end{array}\right]=\left[\begin{array}{l}b_1 \ b_2 \ b_3\end{array}\right]$
$A \cdot X=B$

We therefore proceed with the following steps called forward elimination.

1. Scale equation 1 by $-a_{21} / a_{11}$ and add it to equation 2 . (Equation 2 is now updated)
2. Scale equation 1 by $-a_{31} / a_{11}$ and add it to equation 3. (Equation 3 is now updated)
3. Scale equation 2 by $-a_{32}{ }^{\prime} / a_{22}$ and add it to equation 3 . (Equation 3 is updated again)
The systems on the left and right show the state of our setup after steps two and three respectively. Note that the hyphens behind the coefficients indicate the number of times their values have been altered by the addition / subtraction operations.
\begin{aligned} a_{11} x_1+a_{12} x_2+a_{13} x_3=b_1 & \ 0+a_{22}{ }^{\prime} x_2+a_{23}{ }^{\prime} x_3=b_2^{\prime} & \rightarrow \ 0+a_{32}{ }^{\prime} x_3+a_{33}{ }^{\prime} x_3=b_3^{\prime} & \begin{array}{c} a_{11} x_1+a_{12} x_2+a_{13} x_3=b_1 \ 0+a_{22}{ }^{\prime} x_2+a_{23}{ }^{\prime} x_3=b_2^{\prime} \ 0+0+a_{33}^{\prime \prime} x_3=b_3^{\prime \prime} \end{array} \ & {\left[\begin{array}{ccc} a_{11} & a_{12} & a_{13} \ 0 & a_{22}^{\prime} & a_{23}{ }^{\prime} \ 0 & 0 & a_{33}^{\prime \prime} \end{array}\right] \cdot\left[\begin{array}{l} x_1 \ x_2 \ x_3 \end{array}\right]=\left[\begin{array}{c} b_1 \ b_2^{\prime} \ b_3^{\prime \prime} \end{array}\right] } \end{aligned}
At the end of the forward elimination step, we reach what is called the row echelon form of matrix $A$. In this form, the leading non-zero element in each row will have zeros placed in the column entries beneath it. The row echelon form also requires that the first non-zero element in any particular row must be positioned to the right compared to the non-zero element of the row above it. The next step is to solve for $x_3$ and back substitute that value into the second equations. To complete the Gaussian elimination procedure, we find $x_2$ and back-substitute both $x_2$ and $x_3$ into equation one to solve for $x_1$.

## 电气工程代写|数字信号过程代写digital signal process代考|Pseudo Inverse for Overdetermined Systems of Linear Equations

In our last example, we found a polynomial curve that passed through four arbitrary points of our choosing. Solving the problem involved finding the inverse of the square matrix $A$. You may ask yourself whether there are situations in which the matrix $A$ would not be square and just what the meaning of such a configuration would be. This situation occurs when the system of linear equations is overdetermined. Such a configuration is actually rather common in the field of DSP and numerical methods. Chapter 3 on optimization will go into great detail regarding the treatment and solution of over-determined systems of linear equations. A simple example will give us a wonderful insight into an application that requires the solution of a linear system of equations that is overdetermined.

Linear regression is a technique in which we attempt to fit a line to a set of observed test values. Let’s assume that we are taking pictures of an object moving across the sky with a digital camera. We know that the path of the object is a straight line across the sky but try as we want, the vibration of the ground, perhaps due to nearby traffic, is causing small amounts of shaking when the camera takes its pictures. Therefore, the position that the camera determined with each exposure includes a random error, which we can’t eliminate. We use linear regression to guess at the true parameters of the line given potentially noisy observations of the objects position in the sky.

# 数字信号过程代考

## 电气工程代写|数字信号过程代写digital signal process代考|Gaussian Elimination

1. 将方程 1 缩放 $-a_{21} / a_{11}$ 并将其添加到等式 2 中。（公式 2 现已更新)
2. 将方程 1 缩放 $-a_{31} / a_{11}$ 并将其添加到方程 3 。（方程 3 现已更新)
3. 缩放方程 $2-a_{32}{ }^{\prime} / a_{22}$ 并将其添加到等式 3 中。 (方程 3 再次更新)
左侧和右侧的系统分别显示了我们在第二步和第三步之后的设置状态。请注意，系数后面的连字符表示它们的值被加法/减法运算改变的次数。
$$a_{11} x_1+a_{12} x_2+a_{13} x_3=b_1 0+a_{22}{ }^{\prime} x_2+a_{23}{ }^{\prime} x_3=b_2^{\prime} \quad \rightarrow 0+a_{32}{ }^{\prime} x_3+a_{33}{ }^{\prime} x_3=b_3^{\prime} a_{11} x_1+a_{12} x_2+a_{13} x_3=b_1 0+a_{22}{ }^{\prime} x_2+a_{23}{ }^{\prime}$$
在前向消除步骙结束时，我们达到了矩阵的行梯形 $A$. 在这种形式中，每行中的前导非零元素将在其下方的列条目中放置零。行梯形形式还要求 任何特定行中的第一个非零元素必须位于其上方行的非零元素的右侧。下一步是解决 $x_3$ 然后将该值代入第二个方程。为了完成高斯消元过程， 我们发现 $x_2$ 和回替代两者 $x_2$ 和 $x_3$ 进入方程一求解 $x_1$.

## 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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