# All Questions

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### Open Source Linear Algebra Library

I am making a code in C that requires the equivalent of Matlab's '\' command for a linear system of the form AX=B where A is an NxN matrix and X, B are Nx1 vectors- i.e a code that performs X=A\B that ...
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### Stability analysis for a hyperbolic PDE on staggered grid

I am trying to understand the stability of a finite difference equation on the staggered grid. I could understand the Von Neumann stability analysis for the collocated grid for a simple acoustic ...
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### Python environments for AMG and Gauss Seidel as solvers instead of preconditioners

I am working on block preconditioning and seemingly it is common to write customised Krylov solvers for them. Within each solver, the individual block linear system with preconditioners are ...
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### Exact distribution of random walk after 10 or 100 steps

(Variant of Stats Exercise to Protect the Innocent). Starting for $x = 0$ I can do one of two operations $\pm 1$ or $\pm 4$. Let $T$ be one iteration of this step. What is the mean and standard ...
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### What is the difference between Computational Science and Data Science?

Background: My PhD was in 'Computational Science'. My dissertation was on the analysis of X-Ray Diffraction Data and analysis of thermally perturbed nuclei in the overall dynamic analysis of the ...
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### CVX problem formulation

Hello, I have a trouble formulating the statement for cvx Matlab package. Here x is a state variable, alpha, c1,c2 - contstants. Ai, Bi, di are matrices depending on Ai-1, Bi-1, di-1. One of the ...
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### Approximating rotation matrix of arbitrary objective function

I want to approximate the rotation in SO(3) (ie. 3D rotation) that minimizes some objective function. I'm looking for a SO(3) rotation representation that lends itself to energy minimization. I'm ...
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### How to flash AMD BIOS chip on automated catheter production machine in factory? [on hold]

this is my first question I hope I make it clear enough and posted in the right section. The automated catheter production machine at the factory I'm doing my internship is down. When turned on there ...
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### Finding an enclosing parabola for a set of points

I am looking for an algorithm that fits a parabola to a set of data points. However, no data point may be below the parabola. All points must be above the parabola. Is there an standard algorithm for ...
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### Array initialization in C

In this bit of code, the X and Y arrays should be identical but for some reason, that I CANNOT figure out for the life of me, X[0] is always 1 rather than 0. I have tried initializing the whole array ...
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### Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
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### Fastest method forfinding a solution to x*log(x)

more specifically, $C x \log_2(x)- K = 0$, where $C$ and $K$ are constants ($\log_2$ means log base 2). I was solving a topcoder problem, SortEstimate, which requires us to solve the aforementioned ...
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### Lanczos algorithms for Hermitian system with toeplitz kernel

Basically I am trying to compute the SVD of a large hermian matrix H using Lanczos iteration, while H consists if a toeplitz kernel K, which should be able to help speed up the matrix-vector ...
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### Interpreting convergence study results, fixed CFL

I am trying to determine the order of my numerical method for resolving a fluid-structure interaction problem using the immersed boundary method. I am using Crank-Nicolson to resolve the fluid ...
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### Small, unpredictable results in runs of a deterministic model

I have a sizable model (~5000 lines) written in C. It is a serial program, with no random number generation anywhere. It makes use of the FFTW library for functions using FFT - I do not know the ...
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### Coupling Boundary Condition of one PDE with source term of another PDE

We have a system of equations, wherein the BC of one PDE is coupled with the source term of another PDE. We have a regular 2D unit grid in x and y. There are two PDEs to be solved The first PDE (...