Please answer the following questions in complete sentences in a typed manuscript and submit the solution on blackboard by on April 11th at noon. (These will be back before the midterm.)
Please identify anyone, whether or not they are in the class, with whom you discussed your homework. This problem is worth 1 point, but on a multiplicative scale.
Make sure you have included your source-code and prepared your solution according to the most recent Piazza note on homework submissions.
The following sequences converge to as :
Indicate the type of convergence for each sequence in terms of
Using any method we've seen to solve a scalar nonlinear equation (bisection, false position, secant), develop a routine to compute using only addition, subtraction, multiplication, and division (and basic control structures) to numerical precision. (Use double-precision.)
Compare the results of your method to the Matlab/Julia/Python function sqrt
.
Comment on any differences that surprise you.
Consider the problem . The only positive real root is located in . Compare the performance of bisection, false position, and the secant method in terms of the number of function evaluations to compute the solution to and full machine precision. For all these methods, use the boundary points (or use those as the first two points for secant).