# Tagged Questions

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### Existence of solution for matrix equation $(I - \alpha A) \bar{x}=\bar{b}$

This is my first question in here and I would be really thankful if someone could help me with understanding the matter. I am solving a matrix equation $(I-\alpha A) \bar{x} = \bar{b}$ for a positive ...
43 views

### Which (approximative) methods are there to compute the inverse of a complicated function?

I have a complicated function $f(x)$ for which I want to compute the inverse $f^{-1}$ over a certain range $R(f): a \leq f(x) \leq b$. The only way to find the inverse I can think of is power series ...
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### Power series and their inverses (radius of convergence of each)

Suppose I have a power series approximation $y$ to an invertible function $f(x)$, and I know that $y$ convergences around $x$ on an interval $(-R,R)$, $R$ being the radius of convergence. How are the ...
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### Does $\exp(\ln(I+A))=I+A$ when $\|A\|<1$?

For matrices, I know certain equalities like $e^{A+B}=e^Ae^B$ aren't always true. I'm curious, do $\exp$ and $\ln$ serve as inverses? I saw earlier that if $\|A\|<1$, then $\ln(I+A)$ converges. My ...
I have a question about the coefficient in the inverse of the power series. Assume $$f=1-\sum_{i=1}^{\infty}(ck_i)x^i,$$ where $c$ and $k_i$ are positive and $0<ck_i<1$ for any $i>0$. ...