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Do they use semidefinite programming in industry?

I can't see any mention of it in job listings. I've seen mentioned integer programming, MIP, mixed-integer nonlinear programming, LP, dynamic programming etc., but no SDP. Is it much trendier in the academy than in industry? From my limited…
GrayOnGray
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How can we evaluate performance of students in computational science courses?

As someone who has to teach courses in computational science, I am confronted with the age-old question: how do I evaluate the ability of the students to learn a subject that depends on applications that are difficult to test with "standard" testing…
aeismail
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Which iterative linear solvers converge for positive semidefinite matrices?

I want to know which of the classic linear solvers (e.g Gauss-Seidel, Jacobi, SOR) are guaranteed to converge for the problem $Ax=b$ where $A$ is positive semi definite and of course $b \in im(A)$ (Notice $A$ is semi definite and not definite)
olamundo
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Sort a cloud of points with respect to an unstructured mesh of hexahedral cells

Question How would you sort a cloud of points with respect to an unstructured mesh of hexahedral cells? Each cell has a centre and a unique label to represent it. There are two cloud points basically (original point cloud, and a point cloud of the…
tmaric
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Policies Relating to Publication and Open Source Development of Code in Academia

Introduction Let me first state some conflicting assertions of the matter to illustrate what are the issues. Personally I would like to have my code open at every stage of development, since others shall see and take advantage of what I am…
Jan
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What is the current state of the art in solving higher dimensional parabolic PDEs (multi-electron Schrödinger equation)

What is the current state of the art for solving higher dimensional (3-10) parabolic PDEs in the complex domain with simple poles (of the form $ \frac{1}{|\vec{r}_1 - \vec{r}_2|}$) and absorbing boundary conditions? Specifically, I'm interested in…
Andrew Spott
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Runge-Kutta and Reusing Datapoints

I am trying to implement the fourth order Runge-Kutta method for solving a first order ODE in Python i.e. $\frac{dy}{dx} = f(x,y)$. I understand how the method works, but am trying to write an efficient algorithm that minimises the number of times…
joshlk
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Computing standard errors for linear regression problems without calculating inverse

Is there a speedier way to calculate standard errors for linear regression problems, than by inverting $X'X$? Here I assume we have regression: $$y=X\beta+\varepsilon,$$ where $X$ is $n\times k$ matrix and $y$ is $n\times 1$ vector. For finding…
mpiktas
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How to establish that an iterative method for large linear systems is convergent in practice?

In computational science we often encounter large linear systems which we are required to solve by some (efficient) means, e.g. by either direct or iterative methods. If we focus on the latter, how can we establish that an iterative method for…
Allan P. Engsig-Karup
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Algebraic Multigrid Code

I would like to understand more details about the implementation of Algebraic Multigrid Methods (AMG). I have been reading "A Multigrid Tutorial", which is quite good and explain all the details of the interpolation, coarse-grid operator and coarse…
Bernardo M. R.
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Why does iteratively solving the Hartree-Fock equations result in convergence?

In the Hartree-Fock self-consistent field method of solving the time-independent electronic Schroedinger equation, we seek to minimize the ground state energy, $E_{0}$, of a system of electrons in an external field with respect to the choice of spin…
James Womack
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Matrix exponential of a skew-Hermitian matrix with fortran 95 and LAPACK

I'm just getting tucked into fortran 95 for some quantum mechanics simulations. Honestly, I've been spoiled by Octave so I've taken matrix exponentiation for granted. Given a (small, $n\leq 36$) skew-Hermitian matrix of size $n\times n$, what is the…
qubyte
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Do black-box preconditioners for matrix-free methods exist?

Jacobian-Free Newton-Krylov (JFNK) methods, and Krylov methods in general, can be very useful because they don't require explicit storage or construction of a matrix, only the results of matrix-vector products. If you do actually form the sparse…
Aurelius
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Least squares approximation question

I am taking a course on scientific computation, and we just went over least squares approximation. My question is specifically about approximating using polynomials. I understand that if you have n+1 data points, you can find a unique polynomial of…
Uday Pramod
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How can I compute a basis for a matrix Lie algebra given a finite set of generators?

Given an arbitrary set of (numerical) square complex matrices $\mathcal{A}=\{A_1,A_2,\cdots,A_m\}$, I am interested in computing the real matrix Lie algebra generated by $\mathcal{A}$, call it $\mathcal{L_\mathcal{A}}$. That is, I would like a basis…
Ian Hincks
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