**Khimich Olexander Mykolaiovych**

Corresponding member of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences, Professor

Tel.: (044) 526 60 88

Tel.: (044) 526 11 96

E-mail: khimich505@gmail.com

#### Brief biography

O.M.Khimich born in 1951 has been working at the V.M.Glushkov Institute of Cybernetics of the NAS of Ukraine since 1973 after graduating from the Faculty of Cybernetics, T.G.Shevchenko Kyiv State University.

Since November 2004 he has been head of a department.

In 1982 he defended his dissertation for the degree of a Candidate of Physical and Mathematical Sciences by the specialty of 01.01.07 – computational mathematics.

In 2002 he was awarded the title of Senior Staff Scientist.

In 2003 he defended his dissertation for the degree of Doctor of Physical and Mathematical Sciences by the specialty of 01.05.02 – mathematical modelling and computational methods.

He is Laureate of the State Prize of Ukraine in the field of science and technology (2011).

In 2014 he was awarded the title of Professor.

In 2015 he was elected Corresponding Member of the National Academy of Sciences of Ukraine.

He published more than 160 scientific papers including 7 monographs and 7 certificates of copyright.

He trained three Candidates of Sciences.

Concurrently he is Professor of the Department of Computational Mathematics of the Faculty of Cybernetics of the Taras Shevchenko Kyiv National University and Department of Automated Information Processing and Control Systems of the Faculty of Informatics and Computing Machines of the NTUU “KPI”; moreover, he delivers lectures by Special courses of “Methods of studying mathematical models with approximate data” and “Methods of parallel computing”.

He is a member of the Academic Council of the Institute of Cybernetics of the NAS of Ukraine and a member of the specialized Scientific Councils for the defence of the dissertations of the Institute of Cybernetics of the NAS of Ukraine (D 26.194.02) and the Institute of Mathematics of the NAS of Ukraine (D 26.206.02).

He is a member of editorial boards of “Journal Numerical and Applied Mathematics” (Numerical Mathematics Series), I.Franko Lviv National University, scientific collection of “Mathematical and Computer Modelling” (town of Kamianets-Podilskyi), scientific collection of “Methods of Optimum Solutions”, Institute of Cybernetics of the NAS of Ukraine (Kyiv city), and “ScienceRise” International scientific journal.

#### Scientific interests

Perturbations and errors theory, numerical methods and computer algorithms, parallel computing methods, numerical software, intelligent information technologies, and mathematical modelling.

#### Main results

The theory of perturbations in linear algebra was developed: estimates of the complete error of solutions of linear systems with approximate data given by direct and iterative methods were derived; the theory of perturbations and the theory of errors for pseudo-inversion and weighted pseudo-inversion problems were developed (estimates for the case of non-matching of the ranks of the output and perturbed matrices were obtained for the first time).

A methodology for the studying of the reliability of computer systems solutions of linear systems (estimation of the closeness of computer solutions to mathematical, hereditary errors due to the approximate nature of the initial data, criteria for the completion of iterative processes guaranteeing this accuracy of approximation to the exact solution) was developed; substantially new results were derived for the case of matrices of incomplete rank.

Some methods of parallel computing and computer algorithms for studying and solving basic problems of computational mathematics with approximate initial data for MIMD computers and hybrid computer (MIMD, SIMD) architectures were developed and studied; a layer and cyclic scheme for the distribution and processing of information on parallel-MIMD-architecture computers was proposed. The scheme entered the practice of parallel computing as tool for constructing balanced parallel algorithms.

Methodology of mathematical modelling for conditionally correct elliptic boundary value problems was developed and substantiated; the fundamental novelty is in the development of an algorithm for calculating a single solution on a subspace without knowledge of the hub of the problem operator; unconverted estimates of the accuracy of finite-difference schemes for fourth order differential operators in generic spaces were obtained.

Some principles, structure and intellectual software for research and solving basic problems of computational mathematics with approximate data for MIMD architecture and hybrid (MIMD, SIMD) architecture were developed.

An economical three-stage algorithm for the calculation of normal pseudo solution and weighted normal pseudo solution with guaranteed accuracy for linear systems with symmetric semi-deterministic semi-deterministic matrices with approximate initial data was proposed.

Some new direct parallel methods for solving linear algebra problems on the basis of structural regularization of sparse matrices were developed and studied.

**Principal scientific and practical results**

Inprakom family of intellectual computers was created and introduced into the production; these were joint development of the Institute of Cybernetics and “Elektronmash” SSPE with the function of automatic adaptive adjustment of the algorithm, program and topologies of the parallel computer to the task’s properties (2005 to 2010). This development was presented at the CEBIT exhibition in Hanover (Germany 2007 and 2008).

The concept, architecture, software and prototype of intelligent parallel computer on multi-core and graphics processors (MIMD, SIMD-architecture) were developed as part of the innovation project of the NAS of Ukraine (2010).

An intelligent parallel workstation of “Inparkom_G” based on multi-core and graphics processors for solving scientific and technical problems with the productivity of 5 T Flops (within the framework of the scientific and technical project of the State Agency for Science, Innovation and Informatization of Ukraine, 2012) was developed.

Intellectual software was established and implemented as regular one for studying and solving tasks with approximate given data and estimates of reliability of computer results for the following MIMD-computers: macro conveyor computer complex MVK ETs 1766 (1990), SCIT supercomputer created by the Institute of Cybernetics (2004 to 2014) and INPARKOM family of intellectual computers (2005 to 2013).

Software-technical and software complexes on the basis of parallel computations for mathematical modelling of processes were developed in the interests of Prof. M.E.Zhukovsky CAI, P.I.Baranov CIAM, and O.M.Krylov CRE.

Information technologies were developed on the basis of parallel computations for mathematical modelling in the sphere of civil and industrial construction and kinetics of the thermal field during welding of metals (2007 and 2008).

Software and hardware complexes for parallel computations based on computers of cluster architecture of the Institute of Cybernetics were created and developed and adapted to the design tasks of the O.K.Antonov ASTC (aerodynamics, durability, design, processing of results etc.).

A number of tasks of mathematical modelling of welding processes and related technologies were solved in cooperation with Ye.O.Paton Institute of Electric Welding of the National Academy of Sciences of Ukraine, in particular, when carrying out scientific and technical project of “Mathematical modelling of the processes of viscous destruction of thick-walled elements of pipelines with thinning defects”.

Intelligent software (intelligent program complexes Inpartool_G and Inparlib_G) was created for the automatic study and solving of computational mathematics problems with approximate input data and estimates of the reliability of the results with the function of automatic adaptive adjustment of the algorithm, programs and topology of the computer to the properties of the task for computers hybrid architecture (on multi-core and graphics processors).

Jointly with the “Electronmash” SSPE a hardware and software complex based on intellectual personal supercomputer of hybrid architecture for mathematical modelling in the defence industry, engineering and construction sectors was created in 2015.

Some new methods and software on the basis of parallel calculations for the study of the boundary state and the resource of safe operation of welded pipelines and pressure vessels (within the framework of the Target Complex Program of Scientific Researches of the NAS of Ukraine “Problems of Resource and Safety of the Exploitation of Structures, Structures and Machines” (“Resource”)” were developed in 2015.