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|
![一道线性代数的题目,英文版的,麻烦用英语做,感激不尽!](/uploads/image/z/3597100-52-0.jpg?t=%E4%B8%80%E9%81%93%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E7%9A%84%E9%A2%98%E7%9B%AE%2C%E8%8B%B1%E6%96%87%E7%89%88%E7%9A%84%2C%E9%BA%BB%E7%83%A6%E7%94%A8%E8%8B%B1%E8%AF%AD%E5%81%9A%2C%E6%84%9F%E6%BF%80%E4%B8%8D%E5%B0%BD%21)
![](http://img.wesiedu.com/upload/1/d6/1d6ba648ac8c00ca0fd7377b12a9675d.jpg)