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Original Articles

A least distance algorithm for a smooth strictly convex norm

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Pages 445-463 | Received 01 Mar 1996, Published online: 19 Mar 2007

References

  • Barrodale , I. and Young , A. 1966 . Algorithms for best L 1 and L∞ linear approximation on a discrete set . Numer. Math. , 8 : 295 – 306 .
  • Cheney , E. W. 1982 . Introduction to Approximation Theory , 2nd edn , New York : McGraw-Hill .
  • Fletcher , R. , Grant , J. A. and Hebden , M. D. 1971 . The calculation of linear best L p approximation . Computer J. , 14 : 276 – 279 .
  • Gill , P. E. , Murray , W. , Saunders , M. A. and Wright , M. H. 1982 . “ Linearly constrained optimization ” . In Nonlinear Optimization 1981 , Edited by: Powell , M. J. D. 123 – 139 . London : Academic Press .
  • Lawson , C. L. and Hanson , R. J. 1974 . Solving Least Squares Problems , Englewood Cliffs, NJ : Prentice Hall .
  • Nikolopoulos , P. V. and Sreedharan , V. P. 1994 . An algorithm for computing non negative minimal norm solutions . Numer. Funct. Anal. and Optimiz. , 15 : 87 – 103 .
  • Nirenberg L. Functional Analysis Lectures given in 1960-61 notes by Lesley Sibner, New York University. 1961
  • Owens , R. W. 1977 . An algorithm for best approximate solutions of Ax = b with a smooth strictly convex norm . Numer. Math. , 29 : 83 – 91 .
  • Owens , R. W. and Sreedharan , V. P. 1989 . An Algorithm for approximation by elements of a cone in a Banach space . Numer. Funct. Anal and Optimiz. , 10 : 1161 – 1189 .
  • Owens , R. W. and Sreedharan , V. P. 1993 . Least squares methods to minimize errors in a smooth, strictly convex norm . J. Approx. Theory , 2 : 180 – 198 .
  • Polak , E. 1971 . Computational Methods in Optimization , New York, NY : Academic Press .
  • Rockafellar , R. T. 1969 . Convex Analysis , Princeton, NJ : Princeton University Press .
  • Späth , H. 1992 . Mathematical Algorithms for Linear Regression , New York, NY : Academic Press .
  • Sreedharan , V. P. 1971 . Least squares algorithms for finding solutions of overdetermined linear equations which minimize error in an abstract norm . Numer. Math. , 17 : 387 – 401 .
  • Sreedharan , V. P. 1973 . Least squares algorithms for finding solutions of overdetermined systems of linear equations which minimize error in a smooth strictly convex norm . J. Approx. Theory , 8 : 46 – 61 .
  • Sreedharan , V. P. 1982 . A subgradient projection algorithm . J. Approx. Theory , 35 : 111 – 126 .
  • Sreedharan , V. P. 1984 . Subgradient projection algorithm II . J. Approx. Theory , 41 : 217 – 243 .
  • Sreedharan , V. P. 1986 . Extensions of subgradient projection algorithms . J. Approx. Theory , 47 : 228 – 239 .
  • Sreedharan , V. P. 1987 . ε-Subgradient projection algorithm . J. Approx. Theory , 51 : 27 – 46 .
  • Sreedharan , V. P. 1987 . An algorithm for a non negative norm minimal solutions . Numer. Funct. Anal. and Optimiz. , 9 : 193 – 232 .
  • Watson , G. A. 1980 . Approximation Theory and Numerical Methods , New York, NY : John Wiley and Sons .
  • Zangwill , W. L. 1969 . Nonlinear Programming: A unified approach , Englewood Cliffs, NJ : Prentice Hall .
  • Zoutendijk , G. 1960 . Methods of Feasible Directions , Amsterdam : Elsevier .

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