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(a) Let X = R² and define P by P (Q)=(Q) Show P is contractive with a = - √2 x₁ = Px₁, x₂ = Px₁ = P²x0, x₁ = Px₂ = P³x,..... What is the value of lim P"x, ? 11-0 (b) Repeat part (a) using P Next, starting with x, = (9)=( JC+0 X₂ -0. calculate

(a) Let X = R² and define P by P (Q)=(Q) Show P is contractive with a = - √2 x₁ = Px₁, x₂ = Px₁ = P²x0, x₁ = Px₂ = P³x,..... What is the value of lim P"x, ? 11-0 (b) Repeat part (a) using P Next, starting with x, = (9)=( JC+0 X₂ -0. calculate

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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# 2. (a) Let X = R² and define P by P ()=(Q) Show P is contractive with a = (b) Repeat part (a) using P √√2 x₁ = Pxo, x₂ = Px₁ = P²x₁, x₂ = Px₂ = P³ xo,.... What is the value of lim P"x, ? 11-400 X₂ (3)=(Q)+0 Next, starting with x, = -0. calculate
Transcribed Image Text:# 2. (a) Let X = R² and define P by P ()=(Q) Show P is contractive with a = (b) Repeat part (a) using P √√2 x₁ = Pxo, x₂ = Px₁ = P²x₁, x₂ = Px₂ = P³ xo,.... What is the value of lim P"x, ? 11-400 X₂ (3)=(Q)+0 Next, starting with x, = -0. calculate
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