1. Problem 1: Find two non-zero roots of the equation sin(z) - z²+1/2 = 0 Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Try to get as many correct digits as you can. Also include timing results for your calcula- tions.

1. Problem 1: Find two non-zero roots of the equation sin(z) - z²+1/2 = 0 Explain how many decimal places you believe you have correct, and how many steps of the bisection method it took. Try to get as many correct digits as you can. Also include timing results for your calcula- tions.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.

Question

Can you use python and show the codes? The second picture was an example in class and the codes used

1. Problem 1: Find two non-zero roots of the equation
sin(x) = x² + 1/2 = 0
Explain how many decimal places you believe you have correct, and
how many steps of the bisection method it took. Try to get as many
correct digits as you can. Also include timing results for your calcula-
tions.

8.8
2
3
10
4
5
6
7
8
9
10
11
12
A 13
14
#Wand a root of f(x) = cos(x) = x
left = 0
right = math.pi/2
f_left = math.cos(left)-left
f_right = math.cos(right) right
for n in range(0, 20):
mid = (left + right)/2
f_mid= math.cos(mid)-mid

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