Questions tagged [efficiency]
The efficiency tag has no usage guidance.
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Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix [duplicate]
As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
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How to leverage the GPU for parallel 3-body problem computations
I have a 3-body simulation which must run millions of times.
As far as I know, the GPU shines when it gets to preform simple operations on huge matrices/arrays. Currently I'm debugging and running my ...
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Single precision vs double precision conjugate gradients
I tested my conjugate gradients implementation with float and double precision and contrary to my guess the double code was twice faster than the single precision code. The reason is that I need many ...
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Efficient heat diffusion implementation with varying coefficients
I have the following heat diffusion equation:
\begin{alignat}{3}
\partial_t u(t, \vec{x}) &= g(\vec{x})\Delta u(t,\vec{x}), &\quad& \vec{x} \in\Omega, \, t\in(0,\infty],\\
\partial_n u(t,\...
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Best approach to simulating dynamics on networks
I have been recently getting into the field of various processes on networks. For example, stochastic processes like percolation, Ising models, various statistical-physics models; or deterministic ...
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Inefficient comparisons of custom data type C++
I've got some code that I need to squeeze every bit of both time and space out of. I'm looking for a better solution to the following problem.
For reasons outside of the scope of this question, I ...
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Dense factorization specialized for RBF-FD method
In RBF-FD methods (see Fornberg & Flyer. A Primer on Radial Basis Functions with Application to the Geosciences. SIAM, 2015. Chapter 5.), the finite-difference stencil coefficients for a set of ...
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Computing pairwise distances in a grid efficiently
I have a spline-based model where I have a set of control points in 3D space. I want to compute pairwise distances between every point on a regular 3D grid and these control points. Is there an ...
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Efficiency of developing PDE solvers using sparse matrices versus loops
I am new to solving PDEs, but have been looking at different implementations of finite difference and finite volume schemes. One thing I have noticed in different implementations is that some ...
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Incomplete Cholesky preconditioner for CG efficiency
I am currently solving the harmonic equation using a P1 FEM discretisation. The resulting matrix $A$ is SPD and fairly sparse so I use a preconditioned conjugate gradients (CG) solver to find a ...
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How asymmetric encryption is done very fast [closed]
In any asymmetric encryption specifications, there is a step where we need to calculate data ^ public_key mod e to get ...
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Solving stiff ODEs: Dealing with Jacobian terms which take too long to compute with finite differences
I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...
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How can I extract the banded or block diagonal part of a sparse matrix in MATLAB?
Given a large sparse (square) matrix in MATLAB, how can I extract the banded or the block-diagonal parts (of fixed size) of it efficiently?
These are useful operations when prototyping and testing ...
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283
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Methods to improve the efficiency and the memory requirement of LU factorization for complex symmetric system matrix
I want to solve a linear set of equations (Ax=b) using LU decomposition. My "A" matrix is a complex matrix which is ...
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Effecient method for iterating over sparse dataset
Apologies if this isn't the appropriate forum for this question.
I have a set of elements that I need to iterate over as part of a modeling workflow. The elements exists over a set of dimensions (i, ...
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