Obliczanie wyznaczników przy analizie obwodów metodą węzłową

The new method of the estimation of precision of the condition number of determinant matrix (CNDM) calculation is worked out. The determinants are used by linear circuits’ analysis with the node method. The estimation of precision is based on the calculus of probability using  Monte-Carlo method. Random change of matrix elements leads to a dispersion value of its determinant. Greater dispersion of determinant means that the matrix is more difficult for the calculations. The new formula for the calculation of condition number of matrix using the product of values of the every entry of the matrix A on its minor was developed. Obtained values of condition number are more accurate comparing to classic values. The accuracy of the new formula was proven with the Monte-Carlo method. The convenience of the usage as value of inaccuracy the number of lost (inaccurate) digits of mantissa versa condition number matrix was shown as added benefit.

Monte-Carlo calculations to determine the required precision matrix determinant is relatively complicated and lengthy process. Therefore author proposed a new formula for the calculation of the condition number of the matrix determinant (CNMD) without the Monte-Carlo calculus.

The method of the control of precision of calculation on the basis of analysis of subtraction is worked out. A new method for improving the precision of the calculation of the determinant of a matrix is proposed. The Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation and of the determinant calculation.

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