1. Use the provided codes of bisection and newton (you have to add comments) to solve numerically a rational function of your choice with both methods.
a. Save in a file last iteration, last result and last error.
b. Plot the error curve for Bisection and Newton in a single figure.
c. Comment (compare performance)
Remark: Take a large initial interval for a better graph quality.
2. Combine both methods to take advantage of the strength of each of them
a. Explain how you perform the coupling
b. Provide the code for the new method
c. Provide the graph of the error for the new method, bisection and Newton on a single figure
d. Comment
Numerical methods are a set of tasks that involve solving numerical equations using arithmetic processes. To find an approximate result, we can pose mathematical questions. The numerical implementation of the problem is the name given to this formulation. Algorithms aren’t required in this case. Then, for numerical implementation, programming logic is created. Programming is frequently done in high-level languages such as Fortran, Basic, and others. This strategy is based on applying the intermediate value property repeatedly. If f(x1) and f(x2) have opposite signs and f(x1) and f(x2) are continuous functions in the closed interval [x1, x2], then there is at least one root in the interval (x1, x2) such that f() = 0.
rtance of establishing a hierarchy became evident during the planning stage of the outdoor management course for the red team, the coordinators within the team assumed leadership roles but were unable to gain positional power due to the team being a peer group (Pettinger, 2007). The leaders selected had little authority and influence over the group as everyone was perceived to have the same rank, status and occupation, hence the leaders had none of French and Ravens five bases of power (Pettinger, 2007). The result was leaders with no positional power over the group, so could not direct the group with the method of leadership required for the situation. The task had significant constraints, particularly a short time frame and a large group size, for this situation Chelladurai recommends an autocratic leadership style would be most favourable (Chelladurai and Madella, 2006). The leaders attempted an autocratic leadership style, setting individual tasks for the group, however due to the poor leader member relations and lack of positional power the leadership structure quickly became a democracy. The product was an extremely unproductive workforce initially because of the time spent discussing how was best to approach the task. Because of how the leaders were perceived by the group there was little mutual trust, respect or confidence that the leaders were making the correct decisions, and as a result any management style they tried to implement would have been unsuccessful (Pettinger, 2007). Ultimately, if the leaders had analysed their position and the group they would have realised this and chosen a more democratic approach initially the group would have gained trust for the leaders, making future policy implementation easier.