메뉴 건너뛰기




Volumn 121, Issue 1, 2000, Pages 37-72

Tutorial history of least squares with applications to astronomy and geodesy

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; CONSTRAINT THEORY; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 0034272687     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00343-5     Document Type: Article
Times cited : (34)

References (53)
  • 1
    • 85120140420 scopus 로고    scopus 로고
    • Å. Björk Numerical Methods for Least Squares Problems 1996 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1996)
    • Björk, Å.1
  • 2
    • 0002016642 scopus 로고
    • On least squares and linear combinations of observations
    • A.C. Aiken On least squares and linear combinations of observations Proc. Roy. Soc. Edinburgh, Section A 55 1934 42 47
    • (1934) Proc. Roy. Soc. Edinburgh, Section A , vol.55 , pp. 42-47
    • Aiken, A.C.1
  • 4
    • 85120131873 scopus 로고
    • L.A. Brown The Story of Maps 1979 Dover New York, NY
    • (1979)
    • Brown, L.A.1
  • 5
    • 0011504608 scopus 로고
    • Curves and surfaces in Euclidean space
    • S.-s. Chern Curves and surfaces in Euclidean space S.-s. Chern Global Differential Geometry, MAA Studies in Mathematics, Vol. 27 1989 Mathematical Association of America Washington, D.C 99 139
    • (1989) , pp. 99-139
    • Chern, S.-s.1
  • 6
    • 85120145416 scopus 로고
    • V. Chvátal Linear Programming 1983 W.H. Freeman New York, NY
    • (1983)
    • Chvátal, V.1
  • 7
    • 0027542045 scopus 로고
    • Circle fitting by linear and nonlinear least squares
    • I.D. Coope Circle fitting by linear and nonlinear least squares J. Optim. Theory Appl. 76 2 1993 381 388
    • (1993) J. Optim. Theory Appl. , vol.76 , Issue.2 , pp. 381-388
    • Coope, I.D.1
  • 8
    • 0012917979 scopus 로고
    • An algorithm for least-squares circle fitting to data with specified uncertainty ellipses
    • M.G. Cox H.M. Jones An algorithm for least-squares circle fitting to data with specified uncertainty ellipses IMA J. Numer. Anal. 9 3 1989 285 298
    • (1989) IMA J. Numer. Anal. , vol.9 , Issue.3 , pp. 285-298
    • Cox, M.G.1    Jones, H.M.2
  • 9
    • 48749149691 scopus 로고
    • A non-iterative method for fitting circular arcs to measured points
    • J.F. Crawford A non-iterative method for fitting circular arcs to measured points Nucl. Instr. and Meth. 211 2 1983 223 225
    • (1983) Nucl. Instr. and Meth. , vol.211 , Issue.2 , pp. 223-225
    • Crawford, J.F.1
  • 10
    • 0042692397 scopus 로고
    • Inductive proof of the simplex method
    • G.B. Dantzig Inductive proof of the simplex method IBM J. Res. Dev. 4 1960 505 506
    • (1960) IBM J. Res. Dev. , vol.4 , pp. 505-506
    • Dantzig, G.B.1
  • 11
    • 85120104641 scopus 로고
    • G.B. Dantzig Linear Programming and Extensions 1963 Princeton University Press Princeton, NJ
    • (1963)
    • Dantzig, G.B.1
  • 12
    • 85120135656 scopus 로고    scopus 로고
    • J.E. Dennis Jr. R.B. Schnabel Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics In Applied Mathematics, Vol. 16 1996 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1996)
    • Dennis, J.E.1    R.B. Schnabel, Jr.2
  • 13
    • 85120123474 scopus 로고
    • J.L.E. Dreyer A History of Astronomy from Thales to Kepler 2nd Edition 1953 Dover New York, NY
    • (1953)
    • Dreyer, J.L.E.1
  • 14
    • 34249771766 scopus 로고
    • Least-squares fitting of circles and ellipses
    • W. Gander G.H. Golub R. Strebel Least-squares fitting of circles and ellipses BIT 34 1994 558 578
    • (1994) BIT , vol.34 , pp. 558-578
    • Gander, W.1    Golub, G.H.2    Strebel, R.3
  • 15
    • 85120140393 scopus 로고    scopus 로고
    • N. Gastinel, Matrices du Second Degré et Normes Générales en Analyse Numérique Linéaire, Thèse d'Etat, Université de Grenoble, 1960.
  • 16
    • 85120131790 scopus 로고    scopus 로고
    • C.F. Gauss, Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1995. (Theory of the Combination of Observations Least Subject to Errors, original with translation by Gilbert W. Stewart).
  • 17
    • 45949115772 scopus 로고
    • A generalization of the Eckart-Young-Mirsky matrix approximation theorem
    • G.H. Golub A. Hoffman G.W. Stewart A generalization of the Eckart-Young-Mirsky matrix approximation theorem Linear Algebra Appl. 88/89 1987 317 327
    • (1987) Linear Algebra Appl. , vol.88/89 , pp. 317-327
    • Golub, G.H.1    Hoffman, A.2    Stewart, G.W.3
  • 18
    • 0000333571 scopus 로고
    • An analysis of the total least squares problem
    • G.H. Golub C.F.V. Loan An analysis of the total least squares problem SIAM J. Numer. Anal. 17 6 1980 883 893
    • (1980) SIAM J. Numer. Anal. , vol.17 , Issue.6 , pp. 883-893
    • Golub, G.H.1    Loan, C.F.V.2
  • 19
    • 85120133088 scopus 로고
    • G.H. Golub C.F.V. Loan Matrix Computations 2nd Edition 1989 Johns Hopkins University Press Baltimore, MD
    • (1989)
    • Golub, G.H.1    Loan, C.F.V.2
  • 20
    • 85120146790 scopus 로고    scopus 로고
    • N. Grossman The Sheer Joy of Celestial Mechanics 1996 Birkhäuser Boston, Cambridge, MA
    • (1996)
    • Grossman, N.1
  • 21
    • 85120106857 scopus 로고    scopus 로고
    • Hewlett-Packard Co., Corvallis Division, 1000 NE Circle Blvd., Corvallis, OR 97330, USA. HP 48G Series User's Guide, 7th edition, March 1994. (Part Number 00048-90126.).
  • 22
    • 85120120093 scopus 로고    scopus 로고
    • N.J. Higham Accuracy and Stability of Numerical Algorithms 1996 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1996)
    • Higham, N.J.1
  • 24
    • 85120110693 scopus 로고
    • R.V. Hogg A.T. Craig Introduction to Mathematical Statistics 4th Edition 1978 Macmillan New York, NY
    • (1978)
    • Hogg, R.V.1    Craig, A.T.2
  • 25
    • 0000491435 scopus 로고
    • Numerical linear algebra
    • W.M. Kahan Numerical linear algebra Canad. Math. Bull. 9 6 1966 757 801
    • (1966) Canad. Math. Bull. , vol.9 , Issue.6 , pp. 757-801
    • Kahan, W.M.1
  • 27
    • 0016927320 scopus 로고
    • A circle fitting procedure and its error analysis
    • I. Kȧsa A circle fitting procedure and its error analysis IEEE Trans. Instr. Meas. 25 1 1976 8 14
    • (1976) IEEE Trans. Instr. Meas. , vol.25 , Issue.1 , pp. 8-14
    • Kȧsa, I.1
  • 28
    • 0032098782 scopus 로고    scopus 로고
    • Computing geodetic coordinates
    • S.P. Keeler Y. Nievergelt Computing geodetic coordinates SIAM Rev. 40 2 1998 300 309
    • (1998) SIAM Rev. , vol.40 , Issue.2 , pp. 300-309
    • Keeler, S.P.1    Nievergelt, Y.2
  • 29
    • 85120113206 scopus 로고
    • C.T. Kelley Iterative Methods for Linear and Nonlinear Equations, Frontiers in Applied Mathematics, Vol. 16 1995 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1995)
    • Kelley, C.T.1
  • 30
    • 85120110918 scopus 로고    scopus 로고
    • D. Kincaid W. Cheney Numerical Analysis: Mathematics of Scientific Computing 1996 Brooks/Cole Pacific Grove, CA
    • (1996)
    • Kincaid, D.1    Cheney, W.2
  • 31
    • 85120141590 scopus 로고    scopus 로고
    • P.S.d. Laplace, Traité de Mécanique Céleste, Durprat, Paris, 1798–1825. (Translated with commentary by Nathaniel Bowditch, Boston, MA, 1829; Chelsea, Bronx, NY, 1966).
  • 32
    • 85120138726 scopus 로고
    • C.L. Lawson R.J. Hanson Solving Least Squares Problems, Classics In Applied Mathematics, Vol. 15 1995 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1995)
    • Lawson, C.L.1    Hanson, R.J.2
  • 33
    • 85120096001 scopus 로고
    • A.M. Legendre Nouvelle méthodes pour la déterminiation des orbites des comètes 1805 Courcier Paris
    • (1805)
    • Legendre, A.M.1
  • 34
    • 0002824680 scopus 로고
    • Symmetric gauge functions and unitarily invariant norms
    • L. Mirsky Symmetric gauge functions and unitarily invariant norms Quart. J. Math. Oxford, Ser. 2 11 41 1960 50 59
    • (1960) Quart. J. Math. Oxford, Ser. 2 , vol.11 , Issue.41 , pp. 50-59
    • Mirsky, L.1
  • 35
    • 0028464879 scopus 로고
    • Computing circles and spheres of arithmetic least squares
    • Y. Nievergelt Computing circles and spheres of arithmetic least squares Comput. Phys. Comm. 81 3 1994 343 350
    • (1994) Comput. Phys. Comm. , vol.81 , Issue.3 , pp. 343-350
    • Nievergelt, Y.1
  • 36
    • 58149322864 scopus 로고
    • The condition of Steffensen's acceleration in several variables
    • Y. Nievergelt The condition of Steffensen's acceleration in several variables J. Comput. Appl. Math. 58 1995 291 305
    • (1995) J. Comput. Appl. Math. , vol.58 , pp. 291-305
    • Nievergelt, Y.1
  • 37
    • 0040097929 scopus 로고    scopus 로고
    • Schmidt-Mirsky matrix approximation with linearly constrained singular values
    • Y. Nievergelt Schmidt-Mirsky matrix approximation with linearly constrained singular values Linear Algebra Appl. 261 1997 207 219
    • (1997) Linear Algebra Appl. , vol.261 , pp. 207-219
    • Nievergelt, Y.1
  • 38
    • 85120093638 scopus 로고    scopus 로고
    • Y. Nievergelt, S.P. Keeler, Computing geodetic coordinates in space, J. Spacecraft Rockets 37 (2000) 293–296.
  • 39
    • 0031538237 scopus 로고    scopus 로고
    • Reading the master: Newton and the birth of celestial mechanics
    • B. Pourciau Reading the master: Newton and the birth of celestial mechanics Amer. Math. Mon. 104 1 1997 1 19
    • (1997) Amer. Math. Mon. , vol.104 , Issue.1 , pp. 1-19
    • Pourciau, B.1
  • 40
    • 0023379285 scopus 로고
    • Direct least-squares fitting of algebraic surfaces
    • V. Pratt Direct least-squares fitting of algebraic surfaces ACM Comput. Graphics 21 4 1987 145 152
    • (1987) ACM Comput. Graphics , vol.21 , Issue.4 , pp. 145-152
    • Pratt, V.1
  • 42
    • 85120130423 scopus 로고
    • W.C. Rheinboldt Methods for Solving Systems of Nonlinear Equations, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 14 1974 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1974)
    • Rheinboldt, W.C.1
  • 43
    • 34250957105 scopus 로고
    • Zur Theorie der linearen und nichtlinearen Integralgleichungen. 1. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener
    • E. Schmidt Zur Theorie der linearen und nichtlinearen Integralgleichungen. 1. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener Math. Ann. 63 1907 433 476
    • (1907) Math. Ann. , vol.63 , pp. 433-476
    • Schmidt, E.1
  • 44
    • 85120138112 scopus 로고    scopus 로고
    • J.P. Snyder, Map Projections — A Working Manual (U.S. Geological Survey Professional Paper 1395). United States Government Printing Office, Washington, D.C. 20402, 1987.
  • 45
    • 0027879547 scopus 로고
    • On the early history of the singular value decomposition
    • G.W. Stewart On the early history of the singular value decomposition SIAM Rev. 35 4 1993 551 566
    • (1993) SIAM Rev. , vol.35 , Issue.4 , pp. 551-566
    • Stewart, G.W.1
  • 46
    • 85120129572 scopus 로고
    • J. Stoer R. Bulirsch Introduction to Numerical Analysis 2nd Edition 1993 Springer New York, NY
    • (1993)
    • Stoer, J.1    Bulirsch, R.2
  • 47
    • 85120111852 scopus 로고
    • G. Strang Introduction to Applied Mathematics 1986 Wellesley-Cambridge Press Wellesley, MA
    • (1986)
    • Strang, G.1
  • 48
    • 85120125683 scopus 로고
    • A.E. Taylor Introduction to Functional Analysis 1958 Wiley New York, NY
    • (1958)
    • Taylor, A.E.1
  • 49
    • 85120093750 scopus 로고
    • B.L. van der Waerden Geometry and Algebra in Ancient Civilizations 1983 Springer New York, NY
    • (1983)
    • van der Waerden, B.L.1
  • 50
    • 85120103218 scopus 로고
    • S. Van Huffel J. Vandewalle The Total Least Squares Problem: Computational Aspects and Analysis 1991 Society for Industrial and Applied Mathematics Philadelphia, PA
    • (1991)
    • Van Huffel, S.1    Vandewalle, J.2
  • 51
    • 85120103311 scopus 로고    scopus 로고
    • C.F. Van Loan Introduction to Scientific Computing 1997 Prentice-Hall Upper Saddle River, NJ
    • (1997)
    • Van Loan, C.F.1
  • 52
    • 0001117305 scopus 로고
    • Das asymptotische Vertielungsgesetz der Eigenwert linearer partieller Differentialgleichungen (mit einer Anwendung auf der Theorie der Hohlraumstrahlung)
    • H. Weyl Das asymptotische Vertielungsgesetz der Eigenwert linearer partieller Differentialgleichungen (mit einer Anwendung auf der Theorie der Hohlraumstrahlung) Math. Ann. 71 1912 441 479
    • (1912) Math. Ann. , vol.71 , pp. 441-479
    • Weyl, H.1
  • 53
    • 85120142198 scopus 로고    scopus 로고
    • J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford Science Publication, Monographs on Numerical Analysis, Oxford University Press, Oxford, UK, paperback edition, 1988.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.