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Let the vector field (x,y)→f(x,y) be Lipschitz in space, let h=0.1, and consider the Euler map g(x, y) := y + hf(x, y). What is the smallest number L≥0 such that g is L-Lipschitz in space whenever f is 3-Lipschitz in space? Hint: You can answer the question directly, but you have also seen at least part of the answer in the lectures and in the lecture notes. Where? a. The mapping g is not necessarily Lipschitz. b. L=0 O c. L=1.3 O d. L=1.7 O e. L=2 O f. L-exp(0.1) g. L-exp(0.3) h. L=3exp(0.1)

Let the vector field (x,y)→f(x,y) be Lipschitz in space, let h=0.1, and consider the Euler map g(x, y) := y + hf(x, y). What is the smallest number L≥0 such that g is L-Lipschitz in space whenever f is 3-Lipschitz in space? Hint: You can answer the question directly, but you have also seen at least part of the answer in the lectures and in the lecture notes. Where? a. The mapping g is not necessarily Lipschitz. b. L=0 O c. L=1.3 O d. L=1.7 O e. L=2 O f. L-exp(0.1) g. L-exp(0.3) h. L=3exp(0.1)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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Let the vector field (x,y)→f(x,y) be Lipschitz in space, let h=0.1, and consider the Euler map g(x, y) := y + hf(x, y). What is the smallest number L≥0 such that g is L-Lipschitz in space whenever f is 3-Lipschitz in space? Hint: You can answer the question directly, but you have also seen at least part of the answer in the lectures and in the lecture notes. Where? The mapping g is not necessarily Lipschitz. b. L=0 a. O c. L=1.3 d. L=1.7 e. L=2 O f. L-exp(0.1) O g. L-exp(0.3) Oh. L=3exp(0.1)
Transcribed Image Text:Let the vector field (x,y)→f(x,y) be Lipschitz in space, let h=0.1, and consider the Euler map g(x, y) := y + hf(x, y). What is the smallest number L≥0 such that g is L-Lipschitz in space whenever f is 3-Lipschitz in space? Hint: You can answer the question directly, but you have also seen at least part of the answer in the lectures and in the lecture notes. Where? The mapping g is not necessarily Lipschitz. b. L=0 a. O c. L=1.3 d. L=1.7 e. L=2 O f. L-exp(0.1) O g. L-exp(0.3) Oh. L=3exp(0.1)
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