E C E 532
University Of Wisconsin - Green Bay
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hw6_532_fall21_solutions E C E 532|VERY HELPFUL
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CS/ECE/ME 532
Homework 6: Iterative Algorithms for Regularized LS
1. Gradient Descent Convergence. Consider the Gradient Descent iteration for solving a standard
least-squares problem with A ∈ R
m×n
, b ∈ R
m, and A has full column rank. Recall that this iteration
begins with some initial x0 and then:
xk+1 = xk − µAT
(Axk − b) for k = 0, 1, . . . (1)
a) We expect the algorithm to converge to x? = (ATA)
−1ATb. Define the error as ek := xk − x?.
Show how to rewrite (1) in...
Exam (elaborations)
hw6_532_fall21_solutions E C E 532|VERY HELPFUL
Last document update:
ago
CS/ECE/ME 532 Homework 6: Iterative Algorithms for Regularized LS 1. Gradient Descent Convergence. Consider the Gradient Descent iteration for solving a standard least-squares problem with A ∈ R m×n , b ∈ R m, and A has full column rank. Recall that this iteration begins with some initial x0 and then: xk+1 = xk − µAT (Axk − b) for k = 0, 1, . . . (1) a) We expect the algorithm to converge to x? = (ATA) −1ATb. Define the error as ek := xk − x?. Show how to rewrite (1) in...
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