Computational Science Stack Exchange
Computational Science Stack Exchange

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1500 questions
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2 answers

Computation of Cholesky factor

So the Cholesky decomposition theorem states that that any real symmetric positive-definite matrix $M$ has a Cholesky decomposition $M= LL^\top$ where $L$ is a lower triangular matrix. Given $M$, we already know there are fast algorithms to…
smilingbuddha
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Numerical Integration - handling NaNs (C / Fortran)

I am dealing with a tricky integral that exhibits NaNs at certain values near zero and at the moment I am dealing with them quite crudely using an ISNAN statement which sets the integrand to zero when this occurs. I have tried this with the NMS…
Josh
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Is there an open source set of ODE solvers for C that use the native C99 complex type?

I've been using GSL as the foundation of many of my simulations, but it's a little bit overkill for my purposes and it defines its own complex type for legacy reasons. Rather than code my own Runge-Kutta ODE solver, which would probably not be very…
qubyte
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Why are systems with clustered eigenvalues easy to solve?

I came across the following slide by Theo Diamandis & Zachary Frangella on what makes the linear system $Ax=b$ easy to solve using the conjugate gradient method. Transcription: CG converges quickly when The condition number of $A$ is small The…
Yaroslav Bulatov
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2 answers

Faster Logistic Function

I've noticed that a fairly significant number of cycles in one of my programs are being consumed by the logistic function: $$f(x)=\frac{1}{1+e^{-x}}$$ Is there a good approximation I can use to reduce the cost of this function?
Richard
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What are the usual steps and checks involved in upgrading a Scientific Computing code, if there is any?

I'm soon going to start a job as a Scientific Computing software developer. My responsibilities as discussed with the manager are as follows: Analyzing/understanding the existing functionalities (numerical algorithms and physical models) in the 2nd…
Dude
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6 answers

How do compression algorithms compress data so fast?

I've come across compression algorithms, I tried creating a simple run-length encoding algorithm but I notice that when I searched other algorithms I was shocked to know that some algorithms can process thousands of megabits per second how is this…
gushkash
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6 answers

What open source tools are available to visualize molecular vibrations?

I would like to visualize a molecular vibration that is not a normal mode. I'd like to present a static, vectorial representation of the motion, and I would like some flexibility in the vector style (size, color etc). I'm also interested in…
Yann
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Arbitrary Accuracy Scalable Rope Simulation

I am trying to simulate a rope object. The formulation I understand is an array of particles, connected by springs. These springs have very large k-values, so that the line deforms, but stretches very little. I have concluded that solving this as…
geometrian
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Algorithms for Large Sparse Integer Matrices

I'm looking for a library that performs matrix operations on large sparse matrices w/o sacrificing numerical stability. Matrices will be 1000+ by 1000+ and values of the matrix will be between 0 and 1000. I will be performing the index calculus…
jgonagle
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What programming language should I choose and why?

I am a mechanical engineer, intermediated/advanced level in MATLAB and MATHEMATICA, and beginner in Python. I intend to get a PhD in aeroelasticity (FEM + CFD) and coding my own program. I intend to do that because I really like to code and it is a…
Riobaldo Tatarana
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How to integrate polynomial expression over 3D 4-node element?

I want to integrate a polynomial expression over a 4-node element in 3D. Several books on FEA cover the case where integrating is performed over an arbitrary flat 4-noned element. The usual procedure in this case is to find Jacobi matrix and use…
danny_23
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Efficient preconditioner for Augmented Lagrangian

I want to solve a non-linear problem with non-linear equality constrains and I'm using a augmented Lagrangian with a penalty regularization term that, as well known, spoils the condition number of my linearized systems (at each Newton iteration I…
Tom
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Should benchmarkings be done at all? What is the point?

I am reading a paper which compares algorithm A versus algorithm B. It shows that algorithm A is faster than algorithm B via benchmarking that shows the CPU time. What is the point of this? Any benchmarking is going to be dependent on the particular…
efwpf
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What is the most efficient way to write 'for' loops in Matlab?

I have read that if, for example, I have a double for loop that runs over the indexes of a matrix, then putting the column running index in the outer loop is more efficient. For example: a=zeros(1000); for j=1:1000 for i=1:1000 a(i,j)=1; …
TensoR
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