Top new questions this week:
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Do you suggest any references (papers, monographs, books) about the philosophy of computational science? Recently, I found out about the following two: Winsberg, E. (2009). Computer simulation and …
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I was reading a book by Simon Haykin on neural networks when I came across the following strong statement (on the pdf’s page 188): “However, we still have a computational complexity that is $\…
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I am trying to compute $\mathbf{X}\mathbf{u}$ for many times in my algorithm, where $\mathbf{X}\in \mathbb{R}^{n\times m}$ and $\mathbf{u} \in \mathbb{R}^{m}$. The problem is that, during the …
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Greatest hits from previous weeks:
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To my knowledge, there are 4 ways to solving a system of linear equations (correct me if there are more): If the system matrix is a full-rank square matrix, you can use Cramer’s Rule; Compute the …
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$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,…
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I am doing a molecular dynamics simulation. I need to assign initial velocities to the atoms. I want to assign the initial velocities which follow the Maxwell-Boltzmann distribution. How do I …
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I’m new to computational science and I already have learned basic methods for integration, interpolation, methods like RK4, Numerov etc on c++ but recently my professor asked me to learn how to use …
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Is there a Fortran subroutine which performs linear interpolation in one-dimenional data? I need something similar to MATLAB function interp1.
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Thomas algorithm can be used to solve a tridiagonal matrix: $$ \begin{bmatrix} {b_ 1} & {c_ 1} & { } & { } & { 0 } \\ {a_ 2} & {b_ 2} & {c_ 2} & { } & { }…
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I was just curious as to why high-order (i.e. greater than 4) Runge–Kutta methods are almost never discussed/employed (at least to my knowledge). I understand it requires greater computational time …
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