Intellectual computer mathematics system inparsolver

The paper considers the intellectual computer mathematics system InparSolver, which is designed to automatically explore and solve basic classes of computational mathematics problems on multi-core computers with graphics accelerators. The problems of results reliability of solving problems with approximate input data are outlined. The features of the use of existing computer mathematics systems are analyzed, their weaknesses are found. The functionality of InparSolver, some innovative approaches to the implementation of effective solutions to problems in a hybrid architecture are described. Examples of applied usage of InparSolver for processes mathematical modeling in various subject areas are given. Nowadays, new more complex objects and phenomena in many subject areas (nuclear energy, mechanics, chemistry, molecular biology, medicine, etc.) are constantly emerging, which are subject to mathematical research on a computer. This encourages the development of new numerical methods and technologies of mathematical modeling, as well as the creation of more powerful computers for their implementation. With the advent and constant development of supercomputers of various architectures, the problems of their effective use, expansion of tasks range should be solved, ensuring the reliability of computer results and increasing the level of intellectual information support for users ‒ specialists in various fields. Today, the issues of solving these problems are given special attention by many specialists in the fields of information technology and parallel programming. The world's leadingscientists in the field of computer technology see the solution to the problems of efficient usage of modern supercomputers in algorithmic software creation that easily adapts to different computer architectures with different types of memory and coprocessors, supports efficient parallelism on millions of cores etc. In addition, improving the efficiency of high-performance computing on modern supercomputers is provided by their intellectualization, transferring to the computer to perform a significant part of the functions (symbolic languages for computer problem statement, research of mathematical models properties, visualization and analysis of tasks results, etc.). The industry of development and usage of intelligent computer technologies is one of the main directions of science and technology development in modern society

Parallel Algorithms for Solving Linear Systems on Hybrid Computers

Introduction. At present, in science and technology, new computational problems constantly arise with large volumes of data, the solution of which requires the use of powerful supercomputers. Most of these problems come down to solving systems of linear algebraic equations (SLAE). The main problem of solving problems on a computer is to obtain reliable solutions with minimal computing resources. However, the problem that is solved on a computer always contains approximate data regarding the original task (due to errors in the initial data, errors when entering numerical data into the computer, etc.). Thus, the mathematical properties of a computer problem can differ significantly from the properties of the original problem. It is necessary to solve problems taking into account approximate data and analyze computer results. Despite the significant results of research in the field of linear algebra, work in the direction of overcoming the existing problems of computer solving problems with approximate data is further aggravated by the use of contemporary supercomputers, do not lose their significance and require further development. Today, the most high-performance supercomputers are parallel ones with graphic processors. The architectural and technological features of these computers make it possible to significantly increase the efficiency of solving problems of large volumes at relatively low energy costs. The purpose of the article is to develop new parallel algorithms for solving systems of linear algebraic equations with approximate data on supercomputers with graphic processors that implement the automatic adjustment of the algorithms to the effective computer architecture and the mathematical properties of the problem, identified in the computer, as well with estimates of the reliability of the results. Results. A methodology for creating parallel algorithms for supercomputers with graphic processors that implement the study of the mathematical properties of linear systems with approximate data and the algorithms with the analysis of the reliability of the results are described. The results of computational experiments on the SKIT-4 supercomputer are presented. Conclusions. Parallel algorithms have been created for investigating and solving linear systems with approximate data on supercomputers with graphic processors. Numerical experiments with the new algorithms showed a significant acceleration of calculations with a guarantee of the reliability of the results. Keywords: systems of linear algebraic equations, hybrid algorithm, approximate data, reliability of the results, GPU computers.

Gauging Your Gratitude

How are you? Let me be more specific. How grateful are you right now? Consider the last 24 hours: How many of these statements are true? I said “thank you” to someone. I did something nice to show my appreciation. I can list lots of people and things that I'm lucky to have in my life. I noticed when someone helped me. I felt a sense of thankfulness. Me? I scored three out of five. Moderately grateful. To the first three items: yes, yes, yes. Just before dinner, I thanked my daughter Lucy for giving the pot on the stove a stir. I bought a holiday gift for someone who helped me troubleshoot a computer problem. Without hesitation, I can list lots of people and things I'm lucky to have in my life. But did I notice when someone helped me? When I replay my day, I realize there were plenty of occasions when I was being helped—but in the moment, I didn't pause and think, “Hey, what a nice thing for you to do!” And can I say that I felt a general sense of thankfulness? My mom likes to say that gratitude is when your cup runs over with what others have done for you. Maybe I should have, but no, I don't recall feeling particularly appreciative in the last day or so.