# Tag Info

Accepted

### Is it possible for user written algorithms to outperform libraries' built-in optimized functions?

Although LAPACK has some incredibly optimized code, it can still be worth it to write your own version in a few cases. The most important reason (and the reason they make you do it in your course). ...
• 1,189
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### The real myth of GPU (specifically CUDA) really speed up FEM/CFD

Here's the deal with GPUs. On a GPU, every single core is slow. Really slow. However, you have thousands of cores. If you can effectively use the thousands of cores at a time, then your algorithm will ...
• 11.6k

### What is the preferred and efficient approach for interpolating multidimensional data?

For the first part of my question, I found this very useful comparison for performance of different linear interpolation methods using python libraries: http://nbviewer.ipython.org/github/pierre-...
• 647
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### How to compare runtimes of two algorithms in a reproducible way

To make more robust comparisons (on linux), you can : 1) On Intel CPUs the turbo overclocks your CPU. This is controlled by the temperature of the CPU, so it can behave differently from one run to ...
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### Increasing computational performance by using 16 bit numbers

There has been considerable recent interest in numerical linear algebra using mixed precision with some combination of 16, 32, 64, and 128 bit floating point arithmetic. For example, a low ...
• 17.6k
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### Beating typical BLAS libraries matrix multiplication performance

Consolidating the comments: No, you are very unlikely to beat a typical BLAS library such as Intel's MKL, AMD's Math Core Library, or OpenBLAS.1 These not only use vectorization, but also (at least ...
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### Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?

I was able to reproduce the behavior reported in the question, and traced the observed inaccuracies to the following line: ...
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• 186

### Performance differences between ATLAS and MKL?

Prior answers to this question have covered most of the salient points, but I want to add one comment with respect to this: does MKL have the upper hand for some tasks? The MKL team is in a unique ...
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### Is it possible for user written algorithms to outperform libraries' built-in optimized functions?

To clarify @ThiysSteel's good answer: The point is not to attempt to surpass the optimization of code written by very experienced people, who'd wrangled with it for decades. The point is to acquaint ...
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### Is it possible for user written algorithms to outperform libraries' built-in optimized functions?

I used to try to optimize code via using assembly language (as opposed to C). I had some clear success, where a real-time microphone array worked with assembly language, but it would not work at all ...
• 171

### Lua and Fortran (or Python) I/O

This is probably not the answer you are looking for, but I wanted to state it anyway: Your choice of programming languages introduces two difficulties you will encounter as your program grows. First,...
• 50.7k
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### Performance of adding eight numbers sequentially vs. in a tree

I think your analysis is basically right. Some notes. 1. Pipelining is the wrong word here; what you're looking at here is data dependency. A CPU pipeline splits an individual instruction into ...
• 11.4k
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### What is the state of the art algorithm for diagonalizing real symmetric matrices?

The QR/Francis algorithm is the go-to choice for dense eigenproblems, but there are a few competitors around: The Jacobi algorithm (like QR, another algorithm with an unfortunate name, which can be ...
• 8,610
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### Why is the speed of the parts of the LU-decomposition so different?

First, don't forget to also time the LU decomposition in a loop! Otherwise it's not really a fair comparison. If I do that, I get the following timings: ...
• 11.9k
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### Implementation of Jacobi iteration

If you really want to speed it up, I'd suggest changing your iteration to a SSOR iteration. This can converge much faster than jacobi, and if you are already OpenMP parallelized, there's not much you ...
• 1,902