Research Information System
WSEAS Conference on Recent Advances in Systems Engineering and Applied Mathematics, İstanbul, Turkey, 27 - 30 May 2008, pp.13
Fluctuationlessness Theorem is a recently created very efficient tool for matrix representations. It dictates us that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function is identical to the the image of the independent variable's matrix representation over the same space via same basis set, under that univariate function. This helps us to create very rapidly converging univariate numerical integration schemes which can be used in many diversive areas of science and engineering. The multivariate counterpart of this theorem has also been conjectured and proven quite recently. In these theorems, the matrix representations are defined on Hilbert spaces which are defined through certainappropriate inner products.