Gaussian quadrature for matrix valued functions on the unit circle.
La elaboración de mapas que incluyen contornos de nivel se hace a partir de un conjunto de puntos dados por sus coordenadas. Existen varias formulaciones analíticas para definir una función de interpolación. En este artículo se propone una variante de la formulación de Little que puede servir para mejorar localmente su funcionamiento. Con objeto de estudiar su rendimiento se describen las alternativas presentes con cuatro ejemplos.
We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.
Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points...