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A) 确定一个近似于以下条件数的表达式功能：
f(x) = e3x2+1

B) 解释条件数很大的含义是什么。

A) 计算对应于 A 的 LU 分解的矩阵 L 和 U（即，A = LU）。 逐步解释您的计算，说明消除矩阵你在每一步使用。

B) 有时 A 的 LU 分解表示为 PA = LU。 这被称为部分旋转。 部分旋转的目的是什么，它是如何执行的？

Question 1 [10 marks = 5 + 5 ]
This question is about errors and computer arithmetic.
A) Determine an expression that approximates the condition number for the following function:
f(x) = e3x2+1

B) Explain what are the implications of the condition number being large.

Question 2 [15 marks = 10 + 5 ]
This question is about linear systems.
A) Compute the matrices L and U that correspond to the LU factorisation of A (i.e.,
A = LU). Explain step by step your computation, stating the elimination matrices you use at each step.

B) Sometimes an LU decomposition of A is expressed as PA = LU. This is known as partial pivoting. What is the purpose of partial pivoting and how is it performed?

Question 3 [10 marks]
This question is about solving non-linear equations. Using pseudocode write down an algorithm to nd the root of a non-linear function f(x) using the Secant method. Your algorithm should use initial guesses x0 and x1, and stop when the absolute error is less than .