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Although we used gradient descent to find the minimizer of f in part (a), we can also use calculus to solve the problem directly. Show that the minimizer of f is âû = (A" A # 71)-'A"b,

Although we used gradient descent to find the minimizer of f in part (a), we can also use calculus to solve the problem directly. Show that the minimizer of f is âû = (A" A # 71)-'A"b,

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 84E: Explain the differences between Gaussian elimination and Gauss-Jordan elimination.
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Consider the following optimisation problem: min f(x), xER" where 1 f (x) | Ax – b||3 + |||3, and where A E R™×n, b € R" are defined as 1 2 1 -1 3 | A 1 1 2 2 -1 -2 1 -2
Transcribed Image Text:Consider the following optimisation problem: min f(x), xER" where 1 f (x) | Ax – b||3 + |||3, and where A E R™×n, b € R" are defined as 1 2 1 -1 3 | A 1 1 2 2 -1 -2 1 -2
Although we used gradient descent to find the minimizer of ƒ in part (a), we can also use calculus to solve the problem directly. Show that the minimizer of f is â = (A" A + 71)-'A"b, where I is the 4 × 4 identity matrix. What is the exact numerical value of âî for the problem in (a) and how does it compare to your result from gradient descent? What to submnit: your working out.
Transcribed Image Text:Although we used gradient descent to find the minimizer of ƒ in part (a), we can also use calculus to solve the problem directly. Show that the minimizer of f is â = (A" A + 71)-'A"b, where I is the 4 × 4 identity matrix. What is the exact numerical value of âî for the problem in (a) and how does it compare to your result from gradient descent? What to submnit: your working out.
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