神马作文网一道线性代数的题目,英文版的,麻烦用英语做,感激不尽!
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一道线性代数的题目,英文版的,麻烦用英语做,感激不尽!
Consider the least squares problem min ||Ax-b||^2 , Where A is a n-by-m matrix (experiment input data), x is the m-by-1 unknown vector (coefficients for the linear model), and b is the given n-by-1 vector (measured data). n>>m. Assume Rank(A)=m. Using what you learned from calculus, find the solution x.
You need to
(1) write out the formula explicitly using entries in A and b.
(2) explain why we prefer "least squares", not min ||Ax-b||^4 , or min max |Ax-b|
Consider the least squares problem min ||Ax-b||^2 , Where A is a n-by-m matrix (experiment input data), x is the m-by-1 unknown vector (coefficients for the linear model), and b is the given n-by-1 vector (measured data). n>>m. Assume Rank(A)=m. Using what you learned from calculus, find the solution x.
You need to
(1) write out the formula explicitly using entries in A and b.
(2) explain why we prefer "least squares", not min ||Ax-b||^4 , or min max |Ax-b|
