Assume that the relation between temperature and time is defined as follows: $T = A^kC$ We can find parameters $A$ and $C$ using the least-square method. The given relation is not linear, but we can circumvent this problem using the following relation between $log(T)$ and $k$: $log(T) = k log(A) + log(C)$ How can I show that because of this transformation, the least-square method, bij approach, minimizes the sum of the squares of relative temperature errors (given that these are small enough)?
Showing that the least-square method minimizes error
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linear-algebra
numerical-linear-algebra