# Tagged Questions

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### Approximation of differential equations

Can someone provide me a good reference about approximation techniques in continous domain (not piecewise nor numerical methods) for differential equations?
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### Linear regression where undershooting isn't as bad as overshooting

Given a set of points $(x_i, y_i)$, least-squares linear regression finds the linear function $L$ such that $$\sum \varepsilon(y_i, L(x_i))$$ is minimized, where $\varepsilon(y, y') = (y-y')^2$ is the ...
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### How to approximate a complex linear homogenous recurrence with constant coefficients with a simple one?

Is there some standard way to approximate a complex linear homogenous recurrence with constant coefficients with a simple one? For example, I might want to approximate  ...
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### Expansions of Hermite functions

I am wondering if someone knows good references. I am looking for expansions of Hermite functions, which gives connections between rates of decay and smoothness of coefficients. Thank you for your ...
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### General bound on a polynomial's root with the largest norm

Is there a general bound on a polynomial's root with the largest norm? When Rouche's theorem is used, it still seems that the polynomial's root with the largest norm still needs to be found if we ...
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### Approximation or calculation of the probability of getting “clumps” when sampling from a uniform distribution

Suppose that there are $n$ independent samples $X_1,X_2,...,X_n$ sampled from the uniform distribution on $[0,1]$ with the pdf $f(x)=1$. Is there a good way to calculate or approximate the ...
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### Spline Theory and Code

On P. Janert's book Data Analysis with Open Source Tools there is a discussion on splines, that they are "constructed from piecewise polynomial functions (typically cubic) that are joined together in ...
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### explicit error bounds for Multivariate interpolation

I want to interpolate a function of $d$ variables over a Cartesian grid, using multivariate interpolation, while characterizing interpolation error in terms of bounds on partial derivatives of the ...
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### Approximating roots of the truncated Taylor series of $\exp$ by values of the Lambert W function

To everyone: don't bother writing up another answer, i'm giving this bounty Antonio's answer. It just doesn't let me yet (24 hours delay). If you map the nth roots of unity $z$ with the function ...