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In a previous paper [4] the following problem was considered: find, in the class of Fourier polynomials of degree n, the one which minimizes the functional:, where ∥·∥ is the L norm, F is the rth derivative of the Fourier polynomial F( x), and f(x) is a given function with Fourier coefficients c. It was proved that the optimal polynomial has coefficients c given by. In this paper we consider the more general functional, which reduces to (0.1) for σ =σ/r!. We will prove that the classical sigma-factor method for the regularization of Fourier polynomials may be obtained by minimizing the functional (0.3) for a particular choice of the weights σ. This result will be used to propose a motivated numerical choice of the parameter σ in (0.1). [ABSTRACT FROM AUTHOR]

An iterative procedure is given which enables effecting a rather small number of permutations to decide, in a great number of cases, if two matrices can, or cannot, be reduced one to the other by means of permutations on the rows and columns. Some examples of application of this algorithm are given. [ABSTRACT FROM AUTHOR]