**Key words: **oilfield equipment, classification, forecasting, chain fractions, linear algebra.

An approach to solving the problem of oilfield equipment state classification, based on the construction of systems of linear algebraic equations of high dimensionality, is considered. A fundamentally new algorithm for solving the systems of linear algebraic equations, using the so-called corresponding chain fractions, which is often referred to as proper C-fractions, is suggested. The proposed algorithm for solving the systems of linear algebraic equations, although based on the classical iterative algorithms of Jacobi and Seidel, belongs to the category of exact algorithms, providing the solving systems in a finite number of operations . It is shown that the developed algorithm allows to solve ill-conditioned systems of linear algebraic equations, as well as systems with random matrices. The efficiency of the algorithm for solving the systems of linear algebraic equations is confirmed by comparison with the algorithms of simple Gauss – Seidel iteration.

References

1. Korovin Ya.S., Tkachenko M.G., Kononov S.V., Oilfield equipment's state diagnostics on the basis of data mining technologies (In Russ.), Neftyanoe

khozyaystvo = Oil Industry, 2012, no. 9, pp. 116–118.

2. Korovin Ya.S., Tkachenko M.G., Method of calculation of coordinates of

height of products in system of contactless definition of raznovysotnosti tvs of

the active zone of the reactor (In Russ.), Izvestiya Yuzhnogo Federal'nogo Universiteta. Tekhnicheskie nauki = Izvestiya SFedU. Engineering sciences, 2010, V. 113, no. 12, pp. 172–178.

3. Korovin Ya.S., Khisamutdinov M.V., Tkachenko M.G., Forecasting of oilfield equipment work conditions with the application of evolutionary algorithms and artificial neural networks (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2013, no. 12, pp. 128–133.

4. Feraud R., Clerot F., Simon J.L. et al., Kalman and neural network approaches for the control of a VP bandwidth in an ATM network, Lecture Notes in Computer Science. Springer-Verlag Gmb., 2000, V. 1815, pp. 0655.

5. Korovin I.S., Khisamutdinov M.V., The application of evolu-tionary algorithms in the artificial neural network training process for the oil-field equipment malfunctions’ forecasting, Proceedings of 2nd International Symposium on Computer, Communication, Control and Automation, Atlantis Press, 2013, pp. 253–257.

6. Korovin I.S., Khisamutdinov M.V., Hybrid method of dynamograms wavelet analysis for oil-production equipment state identification, Advanced Materials Research, V. 909, pp. 252–259.

7. Shmoylov V.I., Nepreryvnye drobi i r/ϕ algoritm (Continued fractions and

r/ϕ algorithm), Publ. of TTI YuFU, 2012, 608 p.

8. Shmoylov V.I., Nepreryvnye drobi. Part. 2: Raskhodyashchiesya nepreryvnye drobi (Continued fractions. Part. 2: Divergent continued fractions), L'vov: Merkator Publ., 2004, 558 p.

9. Rutiskhauzer G., Algoritm chastnykh i raznostey (The algorithm of private

and differences) (tr. from German), Moscow: IIL Publ., 1960, 93 p.

10. Shmoylov V.I, Kovalenko V.B., Some applications of the summation algorithm of divergent continued fractions (In Russ.), Vestnik Yuzhnogo nauchnogo tsentra RAN, 2012, V. 8, no. 4, pp. 3–13.

11. Shmoylov V.I., Savchenko D.I., Some applications of the summation algorithm of continued fractions, Algoritm summirovaniya raskhodyashchikhsya nepreryvnykh drobey (In Russ.), Vestnik Voronezhskogo gosudarstvennogo universiteta. Ser. Fizika. Matematika, 2013, no. 2, pp. 258–276.

**Key words: **oilfield equipment, classification, forecasting, chain fractions, linear algebra.

An approach to solving the problem of oilfield equipment state classification, based on the construction of systems of linear algebraic equations of high dimensionality, is considered. A fundamentally new algorithm for solving the systems of linear algebraic equations, using the so-called corresponding chain fractions, which is often referred to as proper C-fractions, is suggested. The proposed algorithm for solving the systems of linear algebraic equations, although based on the classical iterative algorithms of Jacobi and Seidel, belongs to the category of exact algorithms, providing the solving systems in a finite number of operations . It is shown that the developed algorithm allows to solve ill-conditioned systems of linear algebraic equations, as well as systems with random matrices. The efficiency of the algorithm for solving the systems of linear algebraic equations is confirmed by comparison with the algorithms of simple Gauss – Seidel iteration.

References

1. Korovin Ya.S., Tkachenko M.G., Kononov S.V., Oilfield equipment's state diagnostics on the basis of data mining technologies (In Russ.), Neftyanoe

khozyaystvo = Oil Industry, 2012, no. 9, pp. 116–118.

2. Korovin Ya.S., Tkachenko M.G., Method of calculation of coordinates of

height of products in system of contactless definition of raznovysotnosti tvs of

the active zone of the reactor (In Russ.), Izvestiya Yuzhnogo Federal'nogo Universiteta. Tekhnicheskie nauki = Izvestiya SFedU. Engineering sciences, 2010, V. 113, no. 12, pp. 172–178.

3. Korovin Ya.S., Khisamutdinov M.V., Tkachenko M.G., Forecasting of oilfield equipment work conditions with the application of evolutionary algorithms and artificial neural networks (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2013, no. 12, pp. 128–133.

4. Feraud R., Clerot F., Simon J.L. et al., Kalman and neural network approaches for the control of a VP bandwidth in an ATM network, Lecture Notes in Computer Science. Springer-Verlag Gmb., 2000, V. 1815, pp. 0655.

5. Korovin I.S., Khisamutdinov M.V., The application of evolu-tionary algorithms in the artificial neural network training process for the oil-field equipment malfunctions’ forecasting, Proceedings of 2nd International Symposium on Computer, Communication, Control and Automation, Atlantis Press, 2013, pp. 253–257.

6. Korovin I.S., Khisamutdinov M.V., Hybrid method of dynamograms wavelet analysis for oil-production equipment state identification, Advanced Materials Research, V. 909, pp. 252–259.

7. Shmoylov V.I., Nepreryvnye drobi i r/ϕ algoritm (Continued fractions and

r/ϕ algorithm), Publ. of TTI YuFU, 2012, 608 p.

8. Shmoylov V.I., Nepreryvnye drobi. Part. 2: Raskhodyashchiesya nepreryvnye drobi (Continued fractions. Part. 2: Divergent continued fractions), L'vov: Merkator Publ., 2004, 558 p.

9. Rutiskhauzer G., Algoritm chastnykh i raznostey (The algorithm of private

and differences) (tr. from German), Moscow: IIL Publ., 1960, 93 p.

10. Shmoylov V.I, Kovalenko V.B., Some applications of the summation algorithm of divergent continued fractions (In Russ.), Vestnik Yuzhnogo nauchnogo tsentra RAN, 2012, V. 8, no. 4, pp. 3–13.

11. Shmoylov V.I., Savchenko D.I., Some applications of the summation algorithm of continued fractions, Algoritm summirovaniya raskhodyashchikhsya nepreryvnykh drobey (In Russ.), Vestnik Voronezhskogo gosudarstvennogo universiteta. Ser. Fizika. Matematika, 2013, no. 2, pp. 258–276.