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3
votes
0answers
70 views
Question about linearization
Given a data matrix $D\in\mathbb{R}^{N \times N}$
Can one construct another matrix $M$ that for all permutation matrices $Q^A$,$Q^B$,
if $[\sum_i\sum_j (Q^A_{ij}D_{ij})]^2 \geq [\sum_i\sum_j ...
1
vote
2answers
74 views
Linear approximation to ln(x) at x = 1, then estimate ln(1.08)
I know that the derivative of $\ln(x)$, or log of whatever base (x) = $(1/x)$ *the original function. If x is a more complicated expression, then the derivative would be $(x'/x)*f(x)$. If I knew the ...
1
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1answer
44 views
Use least squares to estimate coefficients in a linear system containing noise
Problem
I have a linear system of the form, $y=Ax+v$, where $v$ is noise. I need to use least squares to estimate the coefficients of the matrix $A$.
Atempt
I made the assumption that the error, $v$, ...
0
votes
3answers
72 views
Linear approximation to $y = \sqrt{1-x}$ at $x=0$, then approximate $\sqrt{0.9}$ and $\sqrt{0.99}$
How do I find this? I know that the derivative of $\sqrt{x}$ is $\frac{1}{2\sqrt{x}}$. Here, I would plug in $(1-x)$ instead of $x$. When $x = 0$, the slope would evaluate to $\dfrac{1}{2}$. I got ...
0
votes
1answer
83 views
Relative error; absolute error divided by real value or approx value?
I have the following function;
$$f(x) = -\frac{x}{2x + 4}\cdot v_r \Rightarrow \hat{f}(x) = -\frac{x}{4}\cdot v_r$$
Because $x$ is very small we can approximate $f(x)$ to $\hat{f}(x)$.
Now the ...
0
votes
1answer
36 views
Which number is larger if f'(x) is a differentiable increasing function for all x?
Suppose is a differentiable increasing function for all x. Which number is the larger and why? or
?
I believe f(x) must be concave up everywhere since the derivative is increasing, but I am not ...
