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1answer
213 views

Approximation of a given function by rational functions

Given a function $1/\sqrt{x^2 -k^2}$ where k is a constant with a small imaginary part, how do you go about constructing a rational approximation? I am interested in the L_p (p=2 or $\infty$) norm of ...
4
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1answer
787 views

Searching for an inhomogeneous diophantine approximation algorithm

Given two nonzero real numbers $x$ and $y$ such that $y/x$ is irrational, a real number $z$ to be approximated, and a tolerance $\epsilon$, what is an algorithm that will provide coprime integers $a$ ...
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3answers
119 views

Determining Roots of a Polynomial with Interval Estimates of Coefficients

Let $f$ be a monic univariate polynomial with real coefficients: $$f_A(x) = x^n + a_{n-1}x^{n-1} + ... + a_{0}$$ The values of $A=(a_{n-1},...,a_0)$ are unknown, but are estimated as ...
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31 views

Approximation with Predefined Topology of Niveau Sets

Problem given are a finite, connected, undirected and, cycle-free graph (i.e. a "tree") $T(V,E)$, of which one of the vertices (w.l.o.g. $v_0$) is defined to be the root. a planar imbedding ...