Sparsity in higher order methods for unconstrained optimization

References

• Bader , B. W. and Kolda , T. G. 2006 . Algorithm 862: MATLAB tensor classes for fast algorithm prototyping . ACM Trans. Math. Softw. , 32 ( 4 ) : 635 – 653 .
   Web of Science ®Google Scholar
• Bader , B. W. and Kolda , T. G. 2007 . Efficient MATLAB computations with sparse and factored tensors . SIAM J. Sci. Comput. , 30 ( 1 ) : 205 – 231 .
   Web of Science ®Google Scholar
• Barrett , R. , Berry , M. , Chan , T. F. , Demmel , J. , Donato , J. , Dongarra , J. , Eijkhout , V. , Pozo , R. , Romine , C. and Van Der Vorst , H. 1994 . Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , Philadelphia , PA : SIAM .
   Google Scholar
• Boisvert , R. F. , Pozo , R. , Remington , K. , Barrett , R. and Dongarra , J. J. 1997 . “ The Matrix Market: A web resource for test matrix collections ” . In In Quality of Numerical Software, Assessment and Enhancement , Edited by: Boisvert , R. F. 125 – 137 . London : Chapman and Hall .
   Google Scholar
• Chang , R.-G. , Chuang , T.-R. and Lee , J. K. 2001 . Parallel sparse supports for array intrinsic functions of Fortran 90 . J. Supercomput. , 18 ( 3 ) : 305 – 339 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 1990 . “ An introduction to the structure of large scale nonlinear optimization problems and the LANCELOT project ” . In Computing Methods in Applied Sciences and Engineering , Edited by: Glowinski , R. and Lichnewsky , A . 42 – 51 . Philadelphia , PA : SIAM .
   Google Scholar
• Davis , T. A. 2005 . Algorithm 849: A concise sparse Cholesky factorization package . ACM Trans. Math. Softw. , 31 ( 4 ) : 587 – 591 .
   Web of Science ®Google Scholar
• Davis , T. A. 2006 . Direct Methods for Sparse Linear Systems , Philadelphia , , PA, USA : SIAM .
   Google Scholar
• Duff , I. S. , Erisman , A. M. and Reid , J. K. 1986 . Direct Methods for Sparse Matrices , New York , NY : Clarendon Press .
   Google Scholar
• George , A. and Liu , J. W. 1981 . Computer Solution of Large Sparse Positive Definite , Englewood Cliffs , NJ : Prentice-Hall .
   Google Scholar
• Gilbert , J. R. , Moler , C. and Schreiber , R. 1992 . Sparse matrices in MATLAB: design and implementation . SIAM J. Matrix Anal. Appl. , 13 ( 1 ) : 333 – 356 .
   Web of Science ®Google Scholar
• Gundersen , G. and Steihaug , T. 2008 . Halley and Newton are on step apart . PAMM , 7 ( 1 ) : 2060011 – 2060012 .
   Google Scholar
• Gundersen , G. and Steihaug , T. 2010 . On large scale unconstrained optimization problems and higher order methods . Optim. Meth. Softw. , 25 : 337 – 358 .
   Web of Science ®Google Scholar
• Gutiérrez , J. M. and Hernández , M. A. 1997 . A family of Chebyshev–Halley type methods in Banach spaces . Bull. Austral. Math. Soc. , 55 : 113 – 130 .
   Web of Science ®Google Scholar
• Knuth , E. E. 1997 . The Art of Computer Programming, Fundamental Algorithms , 3 , Vol. 1 , Reading , MA : Addison-Wesley .
   Google Scholar
• Landry , W. 2003 . Implementing a high performance tensor library . Scient. Program. , 11 ( 4 ) : 273 – 290 .
   Google Scholar
• Lin , C.-Y. , Liu , J.-S. and Chung , Y.-C. 2002 . Efficient representation scheme for multidimensional array operations . IEEE Trans. Comput , 51 ( 3 ) : 327 – 345 .
   Web of Science ®Google Scholar
• Lin , C.-Y. , Chung , Y.-C. and Liu , J.-S. 2003 . Efficient data compression methods for multidimensional sparse array operations based on the EKMR scheme . IEEE Trans. Comput. , 52 ( 12 ) : 1640 – 1646 .
   Web of Science ®Google Scholar
• Rose , D. J. 1972 . “ A graph-theoretical study of the numerical solution of sparse positive definite systems of linear equations ” . In Graph Theory and Computing , Edited by: Read , R. C. 183 – 217 . New York : Academic Press .
   Google Scholar
• Saad , Y. 2003 . Iterative Methods for Sparse Linear Systems , Philadelphia , PA : SIAM .
   Google Scholar
• Schwetlick , H. 1979 . “ Numerische Lösung nichtlinearer Gleichungen ” . München-Wien : R. Oldenbourg Verlag .
   Google Scholar