Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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

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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 60EQ
See similar textbooks
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

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS