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Numerical algorithms for problems in analysis and algebra, scientific computation

3 votes
1 answer
349 views

A good starting position for maximizing a function with Newton-Raphson / Halley's method

I'm attempting to find the maximum of this function: \begin{align*} h(\mathbf{t}) = -\left\{\sum_{i=1}^{n}\lambda_i e^{\boldsymbol{\theta}_i^\intercal \mathbf{t}}\right\} + \boldsymbol{\alpha}^\inter …
1 vote
0 answers
93 views

Integral of exponential of quadratics + exponentials

Eq 2 of this paper states this integral: \begin{align*} r^{-\beta} = \frac{1}{\Gamma(\beta)}\int_{-\infty}^{\infty} e^{-re^t + \beta t} dt \end{align*} Is there is name for this identity, or the class …
1 vote
0 answers
437 views

Multivariate solution to Lambert W / product-log function

Consider solving the following system for $x$ \begin{align*} a - b e^{\theta x} - cx = 0 \end{align*} According to your favorite computer algebra program, one possible (and the simplest) is \begin{al …