Solution Found!
Let A and A?1 be as follows: The eigenvalues of A are
Chapter 6, Problem 4E(choose chapter or problem)
Problem 4E
Let A and A−1 be as follows:
The eigenvalues of A are approximately 84.74, 0.2007, and 0.0588.
(a) Approximate ||A||, ||A−1||, and cond(A). (Note Exercise 3.)
(b) Suppose that we have vectors x and ˜x such that Ax = b and ||b − A|| ≤ 0.001. Use (a) to determine upper bounds for || − A−1b|| (the absolute error) and || − A−1b||/||A−1b|| (the relative
error)
Exercise 3 Prove that if B is symmetric, then ||B|| is the largest eigenvalue of B.
Questions & Answers
QUESTION:
Problem 4E
Let A and A−1 be as follows:
The eigenvalues of A are approximately 84.74, 0.2007, and 0.0588.
(a) Approximate ||A||, ||A−1||, and cond(A). (Note Exercise 3.)
(b) Suppose that we have vectors x and ˜x such that Ax = b and ||b − A|| ≤ 0.001. Use (a) to determine upper bounds for || − A−1b|| (the absolute error) and || − A−1b||/||A−1b|| (the relative
error)
Exercise 3 Prove that if B is symmetric, then ||B|| is the largest eigenvalue of B.
ANSWER:
Solution
Step 1 of 3
In this problem, we have to find the approximate ||A||, ||A−1||, and cond(A).
b) we have to determine the upper bound for || − A−1b|| and || − A−1b||/||A−1b||
