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How should errors be reported in scientific libraries?

There are many philosophies in different software engineering disciplines about how libraries should cope with errors or other exceptional conditions. A few of the ones I've seen: Return an error code with the result returned by a pointer argument.…
Daniel Shapero
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CVXOPT VS. OpenOpt

CVXOPT: http://abel.ee.ucla.edu/cvxopt/index.html OpenOpt: http://openopt.org/Welcome What's the relation between them? What are the advantages/disadvantages of them, respectively? BTW, is there any other high quality general purpose convex…
updogliu
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Numerical evaluation of highly oscillatory integral

In this advanced course on applications of complex function theory at one point in an exercise the highly oscillatory integral $$I(\lambda)=\int_{-\infty}^{\infty} \cos (\lambda \cos x) \frac{\sin x}{x} d x$$ has to be approximated for large values…
doetoe
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Fastest PCA algorithm for high-dimensional data

I would like to perform a PCA on a dataset composed of approximately 40 000 samples, each sample displaying about 10 000 features. Using Matlab princomp function consistently takes over half an hour at which point I kill the process. I would like…
mellow
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Sensitivity of BFGS to initial Hessian approximations

I'm trying to implement the Broyden-Fletcher-Goldfarb-Shanno method to find the minimum of a function. I need two initial guesses $x_{-1}$ & $x_0$ and an initial Hessian Matrix approximation $B_0$. The only requirements I find for $B_0$ is that if…
Paul
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Solution of quartic equation

Is there a open C-implementation for the solution of quartic equations: $$ax⁴+bx³+cx²+dx+e=0$$ I am thinking of an implementation of Ferrari's solution. On Wikipedia I read that the solution is computational stable only for some of the possible sign…
highsciguy
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Under what circumstances is Monte Carlo integration better than quasi-Monte Carlo?

A simple enough question: to do a multidimensional integral, given that one has decided that some sort of Monte Carlo method is appropriate, is there any advantage that a regular MC integration using pseudorandom numbers has over a quasi-Monte Carlo…
David Z
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What is the reason that LAPACK uses $\tau$ in QR decomposition (instead of normalizing the reflection vector)?

LAPACK's QR routine stores Q as Householder reflectors. It scales the reflection vector $v$ with $1/v_1$, so the first element of the result becomes $1$, so it doesn't have to be stored. And it stores a separate $\tau$ vector, which contains the…
geza
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Numerically Recovering Imaginary Part of Analytic Continuation from Real Part

My situation. I have a function of a complex variable $f(z)$ defined through a complicated integral. What I am interested in is the value of this function on the imaginary axis. I have numerical access to this function on the following ribbon:…
Arturo don Juan
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Matrix exponential of a Hamiltonian matrix

Let $A, G, Q$ be real, square, dense matrices. $G$ and $Q$ are symmetric. Let $$H = \begin{bmatrix} A & -G \\ -Q &-A^T \end{bmatrix}$$ be a Hamiltonian matrix. I want to compute the matrix exponential of $H$. I need the full matrix exponential,…
DerZwirbel
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Eigenvalue decomposition of the sum: A (symmetric) + D (diagonal)

Suppose $A$ is a real symmetric matrix and its eigenvalue decomposition $V \Lambda V^T$ is given. It is easy to see what happens with the eigenvalues of the sum $A + cI$ where $c$ is a scalar constant (see this question). Can we draw any conclusion…
Ivan
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Solving huge dense linear system?

Is there any hope in solving the following linear system efficiently with an iterative method? $A \in \mathbb{R}^{n \times n}, x \in \mathbb{R}^n, b \in \mathbb{R}^n \text{, with } n > 10^6$ $Ax=b$ with $ A=(\Delta - K) $, where $\Delta$ is a very…
yon
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First appearance of the phrase "inverse crime"

In research on inverse problems, it's common to construct a synthetic data set from a known set of parameters and then test whether the inversion technique can reconstruct those parameters. In doing so, it's important to add appropriate levels of…
Brian Borchers
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Thrust for GPU programming

I'm very new to GPGPU programming so please forgive me if the question is not particularly appropriate. From what I understand GPU programming is a very intricate piece of engineering work when compared to usual CPU programming. One has to be very…
mmirzadeh
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Guides on Python for shared-memory Parallel Programming

I have experience in coding OpenMP for Shared Memory machines (in both C and FORTRAN) to carry out simple tasks like matrix addition, multiplication etc. (Just to see how it competes with LAPACK). I know OpenMP enough to carry out simple tasks…
Inquest
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