Accession Number : AD0655445

Title :   THE STRUCTURE OF POLYNOMIAL AND FOURIER COEFFICIENT MATRICES.

Descriptive Note : Technical rept.,

Corporate Author : NORTHWESTERN UNIV EVANSTON ILL DEPT OF GEOLOGY

Personal Author(s) : Krumbein,W. C.

Report Date : JUN 1967

Pagination or Media Count : 9

Abstract : Current methods of trend analysis utilize mainly the polynomial and Fourier models, both of which are derived from the general linear model. The coefficient matrices associated with the map models are conventionally structured diagonally for polynomials and in blocks for Fourier surfaces. It is possible, however, to consider the elements of such matrices as occupying points in a 'coefficient space' defined by coordinate axes representing the coefficient subscripts. This space may be subdivided in various ways to yield configurations by diagonals, blocks, circles, hyperbolas, etc. Each of these classifications gives rise to a set of ranked map surfaces (sequential or cumulative) that can be used with both map models for expressing and analyzing map data in different ways, and for screening out selected components for map comparisons. (Author)

Descriptors :   (*MAPPING, MATHEMATICAL MODELS), (*MAPS, SURFACES), MATRICES(MATHEMATICS), GEOLOGY, POLYNOMIALS, BEACHES, MATHEMATICAL ANALYSIS

Subject Categories : Cartography and Aerial Photography
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE