Method for solving one-parameter linear equations based on differential transformations
The relevance of the research is caused by the need to develop a new efficient method for defining continuous solutions of one-parametric linear matrix equations, often found in various studies, such as identification of electromechanical energy transformer parameters, optimization of electrical cir...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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Tomsk Polytechnic University
2019-05-01
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| Series: | Известия Томского политехнического университета: Инжиниринг георесурсов |
| Subjects: | |
| Online Access: | http://izvestiya.tpu.ru/archive/article/view/1597 |
| _version_ | 1797813338966589440 |
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| author | Sargis Simonyan Ruben Papovyan |
| author_facet | Sargis Simonyan Ruben Papovyan |
| author_sort | Sargis Simonyan |
| collection | DOAJ |
| description | The relevance of the research is caused by the need to develop a new efficient method for defining continuous solutions of one-parametric linear matrix equations, often found in various studies, such as identification of electromechanical energy transformer parameters, optimization of electrical circuits parameter, registration and processing of borehole geophysics measurements, etc. The aim of the research is to develop a simple constructive numerical-analytical method for determining the solution of the mentioned class of problems, which is easy to implement by the modern information technology. The investigation methods. For solving the considered problems, the authors have applied the method of matrix linear algebra, matrix theory method, as well as the direct and inverse differential transforms of G.E. Pukhov, which differ from the well-known integral transforms by rather positive characteristics - a differentiating operation instead of integrating operations (direct transformation) and a summing operation instead of integrating operation (inverse transformation). The results. The authors proposed the constructive numerical-analytical method for solving one-parametric linear matrix equations by using differential transformation. In this case, the solution of the original continuous problem is actually reduced to solving the recurrent chain of some linear systems of algebraic equations by numerical invariant hypermatrix and hypervectors of free members of the right parts, when the matrix discretes for solving the original problem are determined. Then, on the basis of a reducing ratio (inverse differential transformations) the continuous solution of the original problem is determined. The paper considers the model example. Solving this example the exact Maclaurin analytical solution confirming the simplicity and the high computational efficiency of the method is obtained by numerical-analytical method. Conclusions. The proposed constructive numerical-analytical method is based on two basic mathematical apparatus - the operating method of differential transformation and information solutions obtained with the recurrence of linear matrix equations to solve the recurrence of equivalent linear systems of algebraic equations in the widespread use works of kronikorov numerical matrices. |
| first_indexed | 2024-03-13T07:50:29Z |
| format | Article |
| id | doaj.art-d801e47036c34ad0a5bddfb5fa71c0a2 |
| institution | Directory Open Access Journal |
| issn | 2500-1019 2413-1830 |
| language | Russian |
| last_indexed | 2024-03-13T07:50:29Z |
| publishDate | 2019-05-01 |
| publisher | Tomsk Polytechnic University |
| record_format | Article |
| series | Известия Томского политехнического университета: Инжиниринг георесурсов |
| spelling | doaj.art-d801e47036c34ad0a5bddfb5fa71c0a22023-06-02T21:06:23ZrusTomsk Polytechnic UniversityИзвестия Томского политехнического университета: Инжиниринг георесурсов2500-10192413-18302019-05-013266Method for solving one-parameter linear equations based on differential transformationsSargis SimonyanRuben PapovyanThe relevance of the research is caused by the need to develop a new efficient method for defining continuous solutions of one-parametric linear matrix equations, often found in various studies, such as identification of electromechanical energy transformer parameters, optimization of electrical circuits parameter, registration and processing of borehole geophysics measurements, etc. The aim of the research is to develop a simple constructive numerical-analytical method for determining the solution of the mentioned class of problems, which is easy to implement by the modern information technology. The investigation methods. For solving the considered problems, the authors have applied the method of matrix linear algebra, matrix theory method, as well as the direct and inverse differential transforms of G.E. Pukhov, which differ from the well-known integral transforms by rather positive characteristics - a differentiating operation instead of integrating operations (direct transformation) and a summing operation instead of integrating operation (inverse transformation). The results. The authors proposed the constructive numerical-analytical method for solving one-parametric linear matrix equations by using differential transformation. In this case, the solution of the original continuous problem is actually reduced to solving the recurrent chain of some linear systems of algebraic equations by numerical invariant hypermatrix and hypervectors of free members of the right parts, when the matrix discretes for solving the original problem are determined. Then, on the basis of a reducing ratio (inverse differential transformations) the continuous solution of the original problem is determined. The paper considers the model example. Solving this example the exact Maclaurin analytical solution confirming the simplicity and the high computational efficiency of the method is obtained by numerical-analytical method. Conclusions. The proposed constructive numerical-analytical method is based on two basic mathematical apparatus - the operating method of differential transformation and information solutions obtained with the recurrence of linear matrix equations to solve the recurrence of equivalent linear systems of algebraic equations in the widespread use works of kronikorov numerical matrices.http://izvestiya.tpu.ru/archive/article/view/1597geoinformation systemsone-parametric linear matrix equationsdifferential transformationsrecurrent chain of linear systems of algebraic equationsmatrix discretecontinuous solution |
| spellingShingle | Sargis Simonyan Ruben Papovyan Method for solving one-parameter linear equations based on differential transformations Известия Томского политехнического университета: Инжиниринг георесурсов geoinformation systems one-parametric linear matrix equations differential transformations recurrent chain of linear systems of algebraic equations matrix discrete continuous solution |
| title | Method for solving one-parameter linear equations based on differential transformations |
| title_full | Method for solving one-parameter linear equations based on differential transformations |
| title_fullStr | Method for solving one-parameter linear equations based on differential transformations |
| title_full_unstemmed | Method for solving one-parameter linear equations based on differential transformations |
| title_short | Method for solving one-parameter linear equations based on differential transformations |
| title_sort | method for solving one parameter linear equations based on differential transformations |
| topic | geoinformation systems one-parametric linear matrix equations differential transformations recurrent chain of linear systems of algebraic equations matrix discrete continuous solution |
| url | http://izvestiya.tpu.ru/archive/article/view/1597 |
| work_keys_str_mv | AT sargissimonyan methodforsolvingoneparameterlinearequationsbasedondifferentialtransformations AT rubenpapovyan methodforsolvingoneparameterlinearequationsbasedondifferentialtransformations |