Suppose an experiment was conducted and the data points (1,3) and (2, 2) were obtained. We would like to fit the linear function y(t) unknown slope. xt where r ER is an (a) Find the value of æ that minimizes the residual in the sense of least-squares, i.e. find the x that minimizes ||r||3 where r := Ax – b is the residual (and A and b represent the matrix and vector of a certain system of equations). (b) Suppose we would like to minimize ||r||| instead of the 2-norm. Write down an equation for x that minimizes ||r||4. (In other words, the solution of your equation should be x, the minimizer of ||r||4. You do NOT have to solve this equation.)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose an experiment was conducted and the data points (1,3) and (2,2) were
obtained. We would like to fit the linear function y(t)
unknown slope.
xt where x ER is an
(a) Find the value of æ that minimizes the residual in the sense of least-squares, i.e.
find the x that minimizes ||r||3 where r := Ax – b is the residual (and A and b
represent the matrix and vector of a certain system of equations).
(b) Suppose we would like to minimize ||r||| instead of the 2-norm. Write down
an equation for x that minimizes||r||1. (In other words, the solution of your
equation should be x, the minimizer of ||r||4. You do NOT have to solve this
equation.)
Transcribed Image Text:Suppose an experiment was conducted and the data points (1,3) and (2,2) were obtained. We would like to fit the linear function y(t) unknown slope. xt where x ER is an (a) Find the value of æ that minimizes the residual in the sense of least-squares, i.e. find the x that minimizes ||r||3 where r := Ax – b is the residual (and A and b represent the matrix and vector of a certain system of equations). (b) Suppose we would like to minimize ||r||| instead of the 2-norm. Write down an equation for x that minimizes||r||1. (In other words, the solution of your equation should be x, the minimizer of ||r||4. You do NOT have to solve this equation.)
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