ABSTRACT Mathematics and computer sciences need suitable methods for numerical
calculations of integrals. Classical methods, based on polynomial
interpolation, have many weak sides: they are useless to interpolate the
function that fails to be differentiable at one point or differs from the shape
of polynomials considerably. We cannot forget about the Runge’s phenomenon. To
deal with numerical interpolation and integration dedicated methods should be
constructed. One of them, called by author the method of Hurwitz-Radon Matrices
(MHR), can be used in reconstruction and interpolation of curves in the plane.
This novel method is based on a family of Hurwitz-Radon (HR) matrices. The
matrices are skew-symmetric and possess columns composed of orthogonal vectors.
The operator of Hurwitz-Radon (OHR), built from that matrices, is described. It
is shown how to create the orthogonal and discrete OHR and how to use it in a
process of function interpolation and numerical integration. Created from the
family of N-1 HR matrices and
completed with the identical matrix, system of matrices is orthogonal only for
vector spaces of dimensions N = 2, 4
or 8. Orthogonality of columns and rows is very significant for stability and
high precision of calculations. MHR method is interpolating the curve point by
point without using any formula of function. Main features of MHR method are:
accuracy of curve reconstruction depending on number of nodes and method of
choosing nodes; interpolation of L points of the curve is connected with
the computational cost of rank O(L);
MHR interpolation is not a linear interpolation.
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