Computational algorithms for linear balance models of intersectoral ecological-economic interaction

Nedashkovskiy, N. A.; Kroshka, T. I.

doi:10.1007/s10559-010-9179-0

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“…The issues raised in the article have appeared in generalised Leontiev-Ford simulations for the macroeconomic balance [1,2] in solving Fredholm integral equations with non-linear nuclei. Contemporary scientific literature lacks publications related to the problem.…”

Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Dorożyński

Nedashkovskyy

2020

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Schemes are presented for calculating tuples of solutions of matrix polynomial equations using continued fractions. Despite the fact that the simplest matrix equations were solved in the second half of the 19th century, and the problem of multiplier decomposition was then deeply analysed, many tasks in this area have not yet been solved. Therefore, the construction of computer schemes for calculating the sequences of solutions is proposed in this work. The second-order matrix equations can be solved by a matrix chain function or iterative method. The results of the numerical experiment using the MatLab package for a given number of iterations are presented. A similar calculation is done for a symmetric square matrix equation of the 2nd order. Also, for the discrete (time) Riccati equation, as its analytical solution cannot be performed yet, we propose constructing its own special scheme of development of the solution in the matrix continued fraction. Next, matrix equations of the n-th order, matrix polynomial equations of the order of non-canonical form, and finally, the conditions for the termination of the iterative process in solving matrix equations by branched continued fractions and the criteria of convergence of matrix branching chain fractions to solutions are discussed.

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Section: Introductionmentioning

confidence: 99%