# Tagged Questions

Questions on numerical analysis/numerical methods; methods for approximately solving various problems that often do not admit exact solutions.

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### approximation of a complex valued real rational function

all. I am now struggling with a approximation problem. Suppose we have a matrix-valued measure $\mathrm{d}\Lambda(\omega)$, with compact support $[a,b]$, then its Cauchy transform is a well-defined ...
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### Is there a numerical method to restore symmetrizability and row-stochasticity in a matrix?

I have a radiation-transfer matrix F that had been computed using some raytracing Monte Carlo method. From physics it is clear that it must be row-stochastic :$\sum_{j=1}^{N}F_{ij}=1$ because energy ...
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### Numerical analysis- Runge Kutta

I have: $$y'(x)= \sin(y); y(0)=1$$ I need to calculate the function values with Runge-Kutta. The range is [0,1]. My problem is that I need to choose the h (=dx) such that the error will be in order ...
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### Understanding what to do for relative error when p = 0 (bisection method)

I noticed this was mentioned in class, but the detail wasn't really given as to how to deal with it (outside of using another error method such as absolute error). Given the relative error of the ...
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### Local truncation error of Euler method

Wikipedia and this book say the local truncation error of Euler method is $O(h^2)$. But this book and A friendly Introduction to Numerical Analysis say it's $O(h)$. Which is correct? I have a similar ...
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### How to find a separating hyperplane?

I know about support vector machine, and it's quadratic programming approach which delivers the best separating hyperplane. My question is: is there a relatively simple algorithm to find a non-...
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### Solving ${c_1}^x+\sqrt{\frac{\log(x)x}{2}}+3\log(x)x \le c_2$

Is there any way to solve $${c_1}^x+\sqrt{\frac{\log(x)x}{2}}+3\log(x)x\le c_2,$$ for $x>1$, $0<c_1<1$, and $0<c_2<<1$? Thanks
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### Scalable QR decomposition algorithm

Suppose one has a processor for QR decomposition of complex matrix of size 4 x 4. So if it is necessary to decompose M x M complex matrix, A, one can represent it as R x R block matrix [Cij] (block ...