Here is an efficient more generalized way of dealing with life

[Amine Moulay Ramdane]

Hello...


I am a white arab and i think i am smart since i have also invented many scalable algorithms and algorithms..

Here is an efficient more generalized way of dealing with life:

You have to efficiently know how to efficiently "abstract" complexity,
and you have to efficiently "reuse" the abstracted complexity, and you have to invent algorithms and scalable algorithms and methods and knowledge and tools that give you the necessary quality and efficiency so that to efficiently deal with complexity. And all this needs good smartness in action.


About mathematics and about abstraction..


I think my specialization is also that i have invented many software algorithms and software scalable algorithms and i am still inventing other software scalable algorithms and algorithms, those scalable algorithms and algorithms that i have invented are like inventing mathematical theorems that you prove and present in a higher level abstraction, but not only that but those algorithms and scalable algorithms of mine are presented in a form of higher level software abstraction that abstract the complexity of my scalable algorithms and algorithms, it is the most important part that interests me, for example notice how i am constructing higher level abstraction in my following tutorial as methodology that, first, permits to model the synchronization objects of parallel programs with logic primitives with If-Then-OR-AND so that to make it easy to translate to Petri nets so that to detect deadlocks in parallel programs, please take a look at it in my following web link because this tutorial of mine is the way of learning by higher level abstraction:


How to analyse parallel applications with Petri Nets


https://sites.google.com/site/scalable68/how-to-analyse-parallel-applications-with-petri-nets

So notice that my methodology is a generalization that solves communication deadlocks and resource deadlocks in parallel programs.

1- Communication deadlocks that result from incorrect use of
event objects or condition variables (i.e. wait-notify
synchronization).


2- Resource deadlocks, a common kind of deadlock in which a set of
threads blocks forever because each thread in the set is waiting to
acquire a lock held by another thread in the set.


This is what interests me in mathematics, i want to work efficiently in mathematics in a much higher level of abstraction, i give you
an example of what i am doing in mathematics so that you understand,
look at how i am implementing mathematics as a software parallel conjugate gradient system solvers that scale very well, and i am presenting them in a higher level of abstraction, this is how i am abstracting the mathematics of them, read the following about it to notice it:

About SOR and Conjugate gradient mathematical methods..

I have just looked at SOR(Successive Overrelaxation Method),
and i think it is much less powerful than Conjugate gradient method,
read the following to notice it:

COMPARATIVE PERFORMANCE OF THE CONJUGATE GRADIENT AND SOR METHODS
FOR COMPUTATIONAL THERMAL HYDRAULICS

https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/055/19055644.pdf?r=1&r=1


This is why i have implemented in both C++ and Delphi my Parallel Conjugate Gradient Linear System Solver Library that scales very well, read my following thoughts about it to understand more:


About the convergence properties of the conjugate gradient method

The conjugate gradient method can theoretically be viewed as a direct method, as it produces the exact solution after a finite number of iterations, which is not larger than the size of the matrix, in the absence of round-off error. However, 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


So i think my Conjugate Gradient Linear System Solver Library
that scales very well is still very useful, read about it
in my writing below:

Read the following interesting news:

The finite element method finds its place in games

Read more here:

https://translate.google.com/translate?hl=en&sl=auto&tl=en&u=https%3A%2F%2Fhpc.developpez.com%2Factu%2F288260%2FLa-methode-des-elements-finis-trouve-sa-place-dans-les-jeux-AMD-propose-la-bibliotheque-FEMFX-pour-une-simulation-en-temps-reel-des-deformations%2F

But you have to be aware that finite element method uses Conjugate Gradient Method for Solution of Finite Element Problems, read here to notice it:

Conjugate Gradient Method for Solution of Large Finite Element Problems on CPU and GPU

https://pdfs.semanticscholar.org/1f4c/f080ee622aa02623b35eda947fbc169b199d.pdf


This is why i have also designed and implemented my Parallel Conjugate Gradient Linear System Solver library that scales very well,
here it is:

My Parallel C++ Conjugate Gradient Linear System Solver Library
that scales very well version 1.76 is here..

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-conjugate-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)

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As you have noticed i have just written above about my Parallel C++ Conjugate Gradient Linear System Solver Library that scales very well, but here is my Parallel Delphi and Freepascal Conjugate Gradient Linear System Solvers Libraries that scale very well:

Parallel implementation of Conjugate Gradient Dense Linear System solver library that is NUMA-aware and cache-aware that scales very well

https://sites.google.com/site/scalable68/scalable-parallel-implementation-of-conjugate-gradient-dense-linear-system-solver-library-that-is-numa-aware-and-cache-aware

PARALLEL IMPLEMENTATION OF CONJUGATE GRADIENT SPARSE LINEAR SYSTEM SOLVER LIBRARY THAT SCALES VERY WELL

https://sites.google.com/site/scalable68/scalable-parallel-implementation-of-conjugate-gradient-sparse-linear-system-solver


Thank you,
Amine Moulay Ramdane.