Community Digest |
Top new questions this week: |
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When does linear system have linearly growing singular values?Suppose $W$ is a large matrix where $i$th smallest singular value grows as $O(i)$. What kind of matrix can $W$ be? For instance, this appears to hold for random matrix with IID entries and for lower-...
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What are some good medium matrices with known eigenvectors?I am trying to test if an eigendecomposition I have is working properly. For this I would like some matrices that are 10x10 (ish) with trivial (or known) eigenvectors and eigenvalues so that I can ...
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Understanding this code to truncate the SVDIn Brunton's and Kutz's data-driven science and engineering book, page $19$, is a description of one way to truncate the SVD of a given matrix I want to understand what the code for the variable <...
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Greatest hits from previous weeks: |
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How large is large for direct solvers?Let us say I want to solve a large sparse linear system. It is said that iterative solvers should be better than direct solvers in this case. But how large is large? What is the exact threshold beyond ...
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stupid + stupid = brilliant in scientific computingI'm interested in examples of very effective methods in scientific computing that are the sum or naive combination of very ineffective or bad ones.
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Constraints involving $\max$ in a linear program?Suppose $$\begin{align*} \min A &\mathrm{vec}(U) \\ &\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n \end{align*}$$ where $U$ is a symmetric $n\times ...
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What are the conceptual differences between the finite element and finite volume method?There is an obvious difference between finite difference and the finite volume method (moving from point definition of the equations to integral averages over cells). But I find FEM and FVM to be very ...
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2D Ising Model in PythonI am trying to calculate the energy, magnetization and specific heat of a two dimensional lattice using the metropolis monte carlo algorithm. ...
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Why is division so much more complex than other arithmetic operations?I recently encountered a case where I needed an integer division operation on a chip that lacked one (ARM Cortex-A8). While trying to research why that must be, I found out that in general division ...
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Computational Complexity of 2D ConvolutionI am using image filtering for an image processing algorithm I'm developing. I'm using a predefined Matlab function to do the convolution, but I'd like to know what the computational complexity is for ...
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