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Original Articles

Splitting methods for quadratic optimization in data analysisFootnote

, &
Pages 289-307 | Received 24 Oct 1995, Published online: 20 Mar 2007

References

  • Akima , H. 1978 . A method of bivariate interpolation smooth surface fitting for irregularly distributed data points . ACM Trans. Math. Software , 4 : 148 – 159 .
  • Anderson E. LAPACK User's Guide et al SIAM Philadelphia 1992
  • Barnhill , R.E. , Birkhoff , G. and Gordon , W.J. 1973 . Smooth interpolation in triangles . J. Approx. Theory , 8 : 114 – 128 .
  • Barnhill , R.E. and Gregory , J.A. 1975 . Compatible smooth interpolation in triangles . J. Approx. Theory , 15 : 214 – 225 .
  • Bunch , J.R. and Parlett , B.N. 1971 . Direct methods for solving symmetric indefinite systems of linear equations . SIAM J. Numerical Anal , 8 : 639 – 655 .
  • Cottle , R.W. , Pang , J.S. and Stone , R.E. 1992 . The Linear Complementarity Problem , San Diego : Academic Press .
  • Cryer , C.W. 1971 . The solution of a quadratic programming problem using systematic overrelaxation . SIAM J. Control , 9 : 385 – 392 .
  • De Leone , R. and Mangasarian , O.L. 1988 . Asyncronous parallel successive over-relaxation for the symmetric linear complementarity problem . Math. Programming , 42 : 347 – 361 .
  • De Pierro , A.R. and Iusem , A.N. 1993 . Convergence properties of iterative methods for symmetric positive semidefinite linear complementarity problems . Math. Oper. Res , 18 : 317 – 333 .
  • De Pierro , A.R. and Lopes , J.M. 1994 . Accelerating iterative algorithms for symmetric linear complementarity problems . Intern. J. Computer Math , 50 : 35 – 44 .
  • Dyn , N. and Ferguson , W.E. 1983 . The numerical solution of equality-constrained quadratic programming problems . Math. Comp , 41 ( 163 ) : 165 – 170 .
  • Fletcher , R. 1987 . Practical Methods of Optimization , Chichester : John Wiley .
  • Galligani , E. 1993 . C1 surface interpolation with constraints . Numerical Algorithms , 5 : 549 – 555 .
  • Galligani , E. and Zanni , L. 1996 . “ Error analysis of elimination methods for equality constrained quadratic programming problems, Numerical Methods and Error Bounds ” . In Mathematical Research , Edited by: Alefeld , G. and Herzberger , J. Vol. 89 , 107 – 112 . Berlin : Akademie Verlag .
  • Galligani , I. , Loli Piccolomini , E. and Ruggiero , V. 1992 . “ Numerical solution of the image restoration problem on a multivector computer ” . In Parallel Computing: Problems, Methods and Applications , Edited by: Messina , P. and Murli , A. 183 – 187 . Amsterdam : Elsevier Science Publishers B.V .
  • Galligani , L. , Loli Piccolomini , E. , Ruggiero , V. and Zama , F. 1994 . A substructuring method for solving the image restoration problem on a multiprocessor sytem . Proceedings of SMS , 94 : 435 – 444 .
  • Galligani , I. and Ruggiero , V. 1993 . Numerical solution of equality-constrained quadratic programming problem on vector-parallel computers . Optimization Methods & Software , 2 : 233 – 247 .
  • Gill , P.E. and Murray , W. 1974 . “ Newton type methods for linearly constrained optimization ” . In Numerical Methods for Constrained Optimization , Edited by: Gill , P.E. and Murray , W. London : Academic Press .
  • Gill , P.E. , Murray , W. , Gill , P.E. , Murray , W. , Saunders , M.A. and Wright , M.H. 1984 . Sparse matrix methods in optimization . SIAM J. Sci. Stat. Comp , 5 : 562 – 589 .
  • P.E. , Gill. , W. , Murray. , M.A. , Saunders. and M.H. , Wright. 1984 . Sparse matrix methods in optimization . SIAM J. Sci. Stat. Comp , 5 : 562 – 589 .
  • Goldfarb , D. and Idnani , A. 1983 . A numerically stable dual method for solving strictly convex quadratic programs . Math. Programming , 27 : 1 – 33 .
  • Klucewicz , I.M. 1978 . A piecewise C$sup;1$esup; interpolant to arbitrarily spaced data, Comput . Graph. Image Process , 8 : 92 – 112 .
  • Lawson , C.L. 1977 . “ Software for C1 surface interpolation ” . In Mathematical Software , Edited by: J.R , Rice. Vol. III , New York : Academic Press .
  • Lin , Y.Y. and Pang , J.S. 1987 . Iterative methods for large convex quadratic programs: a survey . SIAM J. Control Optim , 25 : 383 – 411 .
  • Loli Piccolomini , E. , Ruggiero , V. and Zama , F. 1994 . “ A domain decomposition method for scattered data approximation on a multiprocessor system ” . In Parallel Computing: Trends and Applications , Edited by: Evans , D.J. , Joubert , G.R. , Peters , F.J. and Trystram , D. 193 – 200 . B.V. Amsterdam : Elsevier Science Publishers .
  • Luo , Z.Q. and Tseng , P. 1992 . Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem . SIAM J. Optimization , 2 : 43 – 54 .
  • Mangasarian , O.L. 1991 . Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problems . SIAM J. Control Optim , 1 : 114 – 122 .
  • Mangasarian , O.L. and De Leone , R. 1987 . Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs . J. Optim. Theory Appl , 54 : 437 – 446 .
  • Medhi , K.T. 1994 . A two-stage successive overrelaxation algorithm for solving the symmetric linear complementarity problem . Math. Programming , 65 : 365 – 380 .
  • Nielson , G.M. 1983 . A method for interpolating scattered data based upon a minimum norm network . Math. Comp , 40 : 253 – 271 .

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