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1. (a) Find an expression for the orthogonal projection of a point x = R onto the convex set B = {z € R¹ : 0 ≤ i ≤ 1 for each i = 1, ...,n}. You need to show your work, and justify your answer. Hint: It might be helpful to sketch B, when n = 2 (i.e., in 2 dimensions), and use the sketch to help you figure out what the projection should be.

1. (a) Find an expression for the orthogonal projection of a point x = R onto the convex set B = {z € R¹ : 0 ≤ i ≤ 1 for each i = 1, ...,n}. You need to show your work, and justify your answer. Hint: It might be helpful to sketch B, when n = 2 (i.e., in 2 dimensions), and use the sketch to help you figure out what the projection should be.

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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1. (a) Find an expression for the orthogonal projection of a point x = R onto the convex set B = {z € R¹ : 0 ≤ i ≤ 1 for each i = 1, ...,n}. You need to show your work, and justify your answer. Hint: It might be helpful to sketch B, when n = 2 (i.e., in 2 dimensions), and use the sketch to help you figure out what the projection should be.
Transcribed Image Text:1. (a) Find an expression for the orthogonal projection of a point x = R onto the convex set B = {z € R¹ : 0 ≤ i ≤ 1 for each i = 1, ...,n}. You need to show your work, and justify your answer. Hint: It might be helpful to sketch B, when n = 2 (i.e., in 2 dimensions), and use the sketch to help you figure out what the projection should be.
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