Lecture 6

Question 1

What is the concept of root finding?

Answer 1

Question 2

Why is solving multivariate non-linear root finding problems much more difficult?

Answer 2

Question 3

What is the Intermediate Value Theorem (IVT)?

Answer 3

Question 4

What is the algorithm of the bisection method?

Answer 4

Question 5

When is a (root finding) method convergent?

Answer 5

Question 6

What is the order of convergence?

Answer 6

Question 7

What can be said about the speed convergence of the bisection method?

Answer 7

Question 8

When does the bisection method produce a unique result?

Answer 8

Question 9

What is the difference between local and global root finding?

Answer 9

Question 10

What is Newtons (root finding) method?

Answer 10

Question 11

What is the convergence rate of Newtons method?

Answer 11

Question 12

What is the main idea behind Fixed Point Iteration (FPI)?

Answer 12

Question 13

What is the convergence rate of FPI? Show how it is derived.

Clearly this does not matter

Answer 13

Question 14

What is the main idea of the Secant method? What is its algorithm?

Answer 14

Question 15

What is the rate of convergence of the Secant Method? How does it compare to Newtons Method?

Answer 15

Question 16

What is the Inverse Quadratic interpolation (root finding)? What is its rate of convergence?

Answer 16

Question 17

What is the main idea of root finding hybrid methods?

Answer 17