Write an executable Jupyter Notebook that explains several algorithms for the root finding techniques: fixed point,...

 

Transcribed Image Text:

Write an executable Jupyter Notebook that explains several algorithms for the root finding techniques: fixed point, bisection, newton-raphson and secant methods. Write the document using Markdown/Latex cells and Julia 1.5 code. Write down any derivations of error estimates or explanations of the algorithm / pseudo code in Latex. Use example functions to illustrate the algorithm, such as from Examples in textbooks or Problems at the end of chapters from our References (e.g. Kreyszig). Provide graphical plots and visualizations of a series of single iterations to illustrate convergence to (or divergence from) a solution. Additionally, to increase the quality of your paper, (a) you may provide motivation for a particular root finding example by discussing a physical case study or application that results in / requires the use of a numerical root finding technique. (b) Also you may include an implementation and discussion of an additional algorithm not discussed in the lectures (bisection, fixed point, Newton-Raphson, secant), such as an adaptive step size technique. (c) Or you may compare the performance of algorithms across different languages R, python, matlab, C/C++, mathematica. Please remember to place a reference listing at the end of your Jupyter Notebook submission. References such as papers, book chapters, private communications, github repositories, etc. Write an executable Jupyter Notebook that explains several algorithms for the root finding techniques: fixed point, bisection, newton-raphson and secant methods. Write the document using Markdown/Latex cells and Julia 1.5 code. Write down any derivations of error estimates or explanations of the algorithm / pseudo code in Latex. Use example functions to illustrate the algorithm, such as from Examples in textbooks or Problems at the end of chapters from our References (e.g. Kreyszig). Provide graphical plots and visualizations of a series of single iterations to illustrate convergence to (or divergence from) a solution. Additionally, to increase the quality of your paper, (a) you may provide motivation for a particular root finding example by discussing a physical case study or application that results in / requires the use of a numerical root finding technique. (b) Also you may include an implementation and discussion of an additional algorithm not discussed in the lectures (bisection, fixed point, Newton-Raphson, secant), such as an adaptive step size technique. (c) Or you may compare the performance of algorithms across different languages R, python, matlab, C/C++, mathematica. Please remember to place a reference listing at the end of your Jupyter Notebook submission. References such as papers, book chapters, private communications, github repositories, etc.

Answer rating: 100% (QA)

ories Sacni given that Sxx xx1 Sxy consider the simple linear regression Model Mi Bo BI X ... View the full answer