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Thread: About Preconditioning Techniques Analysis for CG Method

Replies: 0
 Posts: 599 Registered: 2/12/10
 About Preconditioning Techniques Analysis for CG Method Posted: Apr 23, 2018 11:57 AM Hello.. As you have noticed i have implemented a new scalable algorithm for my Scalable Parallel C++ and Delphi Conjugate Gradient Linear System Solver Library, why i have choosen Conjugate Gradient ? here is also why: For instance, Conjugate Gradient is known to converge to the exact solution in n steps for a matrix of size n, and was historically first seen as a direct method because of this. However, after a while people figured out that it works really well if you just stop the iteration much earlier - often you will get a very good approximation after much fewer than n steps. In fact, we can analyze how fast Conjugate gradient converges. The end result is that Conjugate gradient is used as an iterative method for large linear systems today. Hope you will be happy with my new scalable algorithm of my following Scalable Parallel C++ Conjugate Gradient Linear System Solver Library, my Scalable Parallel C++ Conjugate Gradient Linear System Solver Library is especially designed for large scale industrial engineering problems that you find on industrial Finite element problems and such, this scalable Parallel library was ported to FreePascal and all the Delphi versions and even to Delphi 7 and also to C++, hope you will find it really good, and it works on Linux and Windows. The Windows version of my Library for both Delphi and C++ supports processors groups so that it can use more than 64 logical processors , and it is NUMA-aware and cache-aware, please look at the source code to notice it. I have just read and understood the following paper about Preconditioning Techniques Analysis for CG Method: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.592.1575&rep=rep1&type=pdf As you have noticed that i have implemented my following Scalable Parallel C++ Conjugate Gradient Linear System Solver Library , it doesn't implement preconditionning techniques because it is fully "scalable" on multicore and NUMA systems, my library contains a Scalable Parallel implementation of Conjugate Gradient Dense Linear System Solver library that is NUMA-aware and cache-aware, and it contains also a Scalable Parallel implementation of Conjugate Gradient Sparse Linear System Solver library that is cache-aware. Please download the zip file and read the readme file inside the zip to know how to use it. Language: GNU C++ and Visual C++ and C++Builder Operating Systems: Windows, Linux, Unix and Mac OS X on (x86) You can download my Scalable Parallel C++ Conjugate Gradient Linear System Solver Library from: https://sites.google.com/site/aminer68/scalable-parallel-c-conjugate-gradient-linear-system-solver-library Thank you, Amine Moulay Ramdane. Edited by: Amine Moulay Ramdane on Apr 23, 2018 12:55 PM Edited by: Amine Moulay Ramdane on Apr 23, 2018 1:20 PM
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