a. The condition number K₂(A) really depends on the choice of the p-norm. It is, e.g., possible that K₁ (A) K∞o (A). b. When solving the linear system Ax=b with an invertible matrix AER dxd for x, the relative error in the output x is at least K₂(A) times the relative error in the input b when both errors are measured in the p-norm. c. When solving the linear system Ax=b with an invertible matrix AER dxd for x, the relative error in the output x is at most Kp(A) times the relative error in the input b when both errors are measured in the p-norm. Od. In view of Proposition 2.16, the formula holds for all p in [1,00] except p=2, and it is false for p=2. Kp (A) = || A||||A¹||p

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Which of the following statements on the condition number are correct? 

 

a. The condition number ₁(A) really depends on the choice of the p-norm. It is, e.g., possible that
K₁ (A) ‡ K∞ (A).
Ob. When solving the linear system Ax=b with an invertible matrix AER
both errors are measured in the p-norm.
C. When solving the linear system Ax=b with an invertible matrix AER
both errors are measured in the p-norm.
d. In view of Proposition 2.16, the formula
holds for all p in [1,00] except p=2, and it is false for p=2.
dxd
for x, the relative error in the output x is at least Kp(A) times the relative error in the input b when
dxd
for x, the relative error in the output x is at most Kp(A) times the relative error in the input b when
Kp(A) = ||A||₂||A¯¹ ||₂
Transcribed Image Text:a. The condition number ₁(A) really depends on the choice of the p-norm. It is, e.g., possible that K₁ (A) ‡ K∞ (A). Ob. When solving the linear system Ax=b with an invertible matrix AER both errors are measured in the p-norm. C. When solving the linear system Ax=b with an invertible matrix AER both errors are measured in the p-norm. d. In view of Proposition 2.16, the formula holds for all p in [1,00] except p=2, and it is false for p=2. dxd for x, the relative error in the output x is at least Kp(A) times the relative error in the input b when dxd for x, the relative error in the output x is at most Kp(A) times the relative error in the input b when Kp(A) = ||A||₂||A¯¹ ||₂
Expert Solution
steps

Step by step

Solved in 3 steps with 23 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,