6 Exercises

• Exercise 1: The determination of a minimum of a function.
• Exercise 2: Derive the interpolation formulas for the line search.
• Exercise 3: The construction of a subroutine for the line search interpolation procedure.
• Exercise 4: Derive the convergence rates for the three sequences mentioned above.
• Exercise 5: Derivative testing.
• Exercise 6: The determination of the two-dimenstional Beale function by numerical techniques.
• Exercise 7: The determination of the roots of a function.
• Exercise 8: The reliability of the root-finding program.
• Exercise 9: The forward and central difference quotients for the determination of a derivative of a function.
• Exercise 10: The minimization of a one-dimensional function by Newton's method.