1936/01/01 by A. C. Aitken · 14 citations
Engineering · Mathematics · #Advanced Statistical Methods and Models #Combinatorics #Computer science #Control Systems and Identification #Degree (music) #Equidistant #Geometry #Least-squares function approximation #Mathematical analysis #Mathematics #Mean squared error #Mean value #Physics #Polynomial #Representation (politics) #Series (stratigraphy) #Set (abstract data type) #Square (algebra) #Statistical and numerical algorithms #Statistics #Uncorrelated #Value (mathematics)
paper · doi:10.1017/s0370164600014346
crossref issued 1936/01/01 · crossref published 1936/01/01 · crossref published-print 1936/01/01 · openalex publication_date 1936/01/01 · crossref published-online 2014/09/15 · crossref created 2015/08/06 · crossref deposited 2019/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01 · crossref indexed 2026/08/01
In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:– (i) The data being u 1 , u 2 , …, u n , the representation is to be given by linear combinations (ii) The linear combinations are to be such as would reproduce any set of values that were already values of a polynomial of degree not higher than the k th. (iii) The sum of squared coefficients which measures the mean square error of y i , is to be a minimum for each value of i .