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0 1 Q4. Let A = for 0 < ɛ <1 small, and let b = a) Calculate the solution x to Ax = b. b) Compute «(A) with respect to the o-norm. c) Let 8b Solve the system Aâu = b + đb and let dx = î – x (with x from part (a)).

0 1 Q4. Let A = for 0 < ɛ <1 small, and let b = a) Calculate the solution x to Ax = b. b) Compute «(A) with respect to the o-norm. c) Let 8b Solve the system Aâu = b + đb and let dx = î – x (with x from part (a)).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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0 1 Q4. Let A = for 0 < ɛ <1 small, and let b: %3D a) Calculate the solution x to Ax = b. b) Compute k(A) with respect to the o-norm. ['] c) Let db Solve the system Aâu = b+ 8b and let d.x = î – x (with x from part (a)). d) Using the results you got in (a)-(c), verify the following inequality we derived in class: ||5x|| ||8|| <K(A)- ||x|| Sa(A) ob|| (1) with || - || is the oo-norm. e) By comparing dx and db, explain why a large condition number k(A) is problem- atic.
Transcribed Image Text:0 1 Q4. Let A = for 0 < ɛ <1 small, and let b: %3D a) Calculate the solution x to Ax = b. b) Compute k(A) with respect to the o-norm. ['] c) Let db Solve the system Aâu = b+ 8b and let d.x = î – x (with x from part (a)). d) Using the results you got in (a)-(c), verify the following inequality we derived in class: ||5x|| ||8|| <K(A)- ||x|| Sa(A) ob|| (1) with || - || is the oo-norm. e) By comparing dx and db, explain why a large condition number k(A) is problem- atic.
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