Introduction

Question 1

Describe the difference between numerical and analytical methods in solving mathematical problems

Answer 1

Numerical methods involve iterative calculations to approximate solutions, while analytical methods derive exact solutions through algebraic manipulations.

Question 2

Describe the relationship between accuracy and precision in numerical methods

Answer 2

Accuracy refers to how closely a computed value agrees with the true value, and precision refers to how closely individual or measured values agree with each other.

Question 3

Which criteria can be used to determine if an iterative method has converged?

Answer 3

The approximate relative error decreases and ultimately is less than the stopping criterion.