Editing Helmert–Wolf blocking (section)

The '''Helmert–Wolf blocking''' ('''HWB''') is a [[least squares]] solution method for the solution of a [[sparse matrix|sparse]] [[block matrix|block]] [[system of linear equations]].<ref>{{cite web|url=http://www.ngs.noaa.gov/GRD/GPS/DOC/gpscom/mca.html|title=Making Combined Adjustments|first=Bill|last=Dillinger|date=4 March 1999|access-date=6 June 2017}}</ref> It was first reported by [[Friedrich Robert Helmert|F. R. Helmert]] for use in [[geodesy]] problems in 1880;<ref>{{cite book|first=Friedrich Robert|last=Helmert|title=Die mathematischen und physikalischen Theorien der höheren Geodäsie, 1. Teil|location=Leipzig|date=1880}}</ref> {{ill|Helmut Wolf (geodesist)|de|Helmut Wolf (Geodät)|lt=H. Wolf}} (1910–1994) published his direct semianalytic solution in 1978.<ref name="wolf-web">{{cite web|url=http://www.fkf.net/Wolf.html|title=The Wolf formulas|date=9 June 2004|accessdate=6 June 2017}}</ref><ref name="wolf">{{cite conference |url= https://archive.org/details/proceedingsofsec00inte|title=The Helmert block method—its origins and development|last1= Wolf|first1= Helmut|date= April 1978|publisher= U.S. Dept. of Commerce|book-title= Proceedings of the second International Symposium on Problems Related to the Redefinition of North American Geodetic Networks|pages= 319–326|location= Arlington, Virginia|conference=International Symposium on Problems Related to the Redefinition of North American Geodetic Networks}}</ref>
It is based on ordinary [[Gaussian elimination]] in [[matrix (mathematics)|matrix]] form<ref name="strang">{{cite book|title=Linear algebra, geodesy, and GPS|url=https://archive.org/details/linearalgebrageo00borr|url-access=limited|first1=Gilbert|last1=Strang|first2=Kai|last2=Borre|date=1997|publisher=Wellesley-Cambridge Press|location=Wellesley|isbn=9780961408862|pages=[https://archive.org/details/linearalgebrageo00borr/page/n265 507]-508}}</ref> or partial [[Mathematical optimization|minimization]] form.<ref name="Leick Rapoport Tatarnikov 2015 p. 673">{{cite book | last1=Leick | first1=A. | last2=Rapoport | first2=L. | last3=Tatarnikov | first3=D. | title=GPS Satellite Surveying | publisher=Wiley | year=2015 | isbn=978-1-119-01828-5 | url=https://books.google.com/books?id=FQlhBgAAQBAJ&pg=PA673 | access-date=2022-01-30 | page=673}}</ref>