From: d@d.d   
      
   Hello,   
      
      
   Read this:   
      
      
   More explanation so that you understand me more..   
      
   You have to understand me more, as you have noticed my opensource   
   software projects are not just opensource projects, because i am taking   
   care of explaining how to use them inside the README file or inside   
   an HTML file when they are too complex, and you can for example notice   
   it with my following software project of my Parallel C++ Conjugate   
   Gradient Linear System Solver Library that scales very well that is very   
   interesting, because i am simplifying the complex mathematics behind it   
   by presenting it to you with my easy C++ interface, the Conjugate   
   Gradient Method is the most prominent iterative method for solving   
   sparse systems of linear equations. Unfortunately, many textbook   
   treatments of the topic are written with neither illustrations nor   
   intuition, and their victims can be found to this day babbling   
   senselessly in the corners of dusty libraries. For this reason, a deep,   
   geometric understanding of the method has been reserved for the elite   
   brilliant few who have painstakingly decoded the mumblings of their   
   forebears. Conjugate gradient is the most popular iterative method for   
   solving large systems of linear equations. CG is effective for systems   
   of the form A.x = b where x is an unknown vector, b is a known vector, A   
   is a known square, symmetric, positive-definite (or positive-indefinite)   
   matrix. These systems arise in many important settings, such as finite   
   difference and finite element methods for solving partial differential   
   equations, structural analysis, circuit analysis, and math homework   
      
   The Conjugate gradient method can also be applied to non-linear   
   problems, but with much less success since the non-linear functions have   
   multiple minimums. The Conjugate gradient method will indeed find a   
   minimum of such a nonlinear function, but it is in no way guaranteed to   
   be a global minimum, or the minimum that is desired.   
   But the conjugate gradient method is great iterative method for solving   
   large, sparse linear systems with a symmetric, positive, definite matrix.   
      
   In the method of conjugate gradients the residuals are not used as   
   search directions, as in the steepest decent method, cause searching can   
   require a large number of iterations as the residuals zig zag towards   
   the minimum value for ill-conditioned matrices. But instead conjugate   
   gradient method uses the residuals as a basis to form conjugate search   
   directions . In this manner, the conjugated gradients (residuals) form a   
   basis of search directions to minimize the quadratic function   
   f(x)=1/2*Transpose(x)*A*x + Transpose(b)*x and to achieve faster speed   
   and result of dim(N) convergence.   
      
      
   And here is My 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.   
      
   Please download the zip file and read the readme file inside the zip to   
   know how to use it.   
      
      
   You can download it from:   
      
   https://sites.google.com/site/scalable68/scalable-parallel-c-con   
   ugate-gradient-linear-system-solver-library   
      
      
   Language: GNU C++ and Visual C++ and C++Builder   
      
   Operating Systems: Windows, Linux, Unix and Mac OS X on (x86)   
      
      
      
      
      
   Thank you,   
   Amine Moulay Ramdane.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)