# Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well

**Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well version 1.76 **

**Author: Amine Moulay Ramdane**

**Description:**

**This library contains a Parallel implementation of Conjugate Gradient Dense Linear System Solver library that is NUMA-aware and cache-aware that scales very well, and it contains also a Parallel implementation of Conjugate Gradient Sparse Linear System Solver library that is cache-aware that scales very well.**

**Sparse linear system solvers are ubiquitous in high performance computing (HPC) and often are the most computational intensive parts in scientific computing codes. A few of the many applications relying on sparse linear solvers include fusion energy simulation, space weather simulation, climate modeling, and environmental modeling, and finite element method, and large-scale reservoir simulations to enhance oil recovery by the oil and gas industry.**

**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. The conjugate gradient method is unstable with respect to even small perturbations, e.g., most directions are not in practice conjugate, and the exact solution is never obtained. Fortunately, the conjugate gradient method can be used as an iterative method as it provides monotonically improving approximations to the exact solution, which may reach the required tolerance after a relatively small (compared to the problem size) number of iterations. The improvement is typically linear and its speed is determined by the condition number κ(A) of the system matrix A: the larger is κ(A), the slower the improvement. **

**Read more here: http://pages.stat.wisc.edu/~wahba/stat860public/pdf1/cj.pdf**

**Please download the zip file and read the readme file inside the zip to know how to use it.**

**You can go to download the zip files by clicking on the following web link:**

**https://drive.google.com/drive/folders/1U3kNVNhcIf7DJOvoSW6IIYjiXIk4_Sfz?usp=sharing**

**Language: GNU C++ and Visual C++ and C++Builder**

**Operating Systems: Windows, Linux, Unix and Mac OS X on (x86)**