P.K. Korneev, A.V. Gladkov

In work representations of determinants of almost triangular matrixes (left and right) in the form of works of final ascending chain fractions are under construction. The received decomposition of determinants can be used for definition of factors of the row which is turning out at division of two meeting sedate ranks; findings of numbers of Bernulli; creation of iterative processes on the basis of the theorem of Kyoniga etc. On the basis of decomposition of determinants of almost triangular matrixes in works of final ascending chain fractions direct methods of the decision of systems of the linear algebraic equations are designed. Is shown that the developed iterative methods on the basis of ascending chain fractions possess property a little to accumulate a computing error, that is these methods possess computing stability. The received methods of the decision of systems with almost triangular matrix can be applied and to the decision of systems of the linear equations with a matrix of a general view, having reduced it previously to system with almost triangular matrix, on an example, Hauskholder's transformation.