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Section B

A fast numerical algorithm for solving nearly penta-diagonal linear systems

, &
Pages 851-860 | Received 14 Oct 2011, Accepted 04 Feb 2012, Published online: 13 Mar 2012

References

  • Batista , M. and Karawia , A. A. 2009 . The use of the Sherman–Morrison–Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations . Appl. Math. Comput , 210 : 558 – 563 .
  • Chen , M. 1987 . On the solution of circulant linear systems . SIAM J. Numer. Anal , 24 : 668 – 683 .
  • Demmel , J. W. 1997 . “ Numerical Linear Algebra ” . Philadelphia , PA : SIAM .
  • Diele , F. and Lopez , L. 1998 . The use of the factorization of five-diagonal matrices by tridiagonal Toeplitz matrices . Appl. Math. Lett , 11 : 51 – 59 .
  • El-Mikkawy , M. and Rahmo , E. 2010 . Symbolic algorithm for inverting cyclic pentadiagonal matrices recursively – derivation and implementation . Comput. Math. Appl , 59 : 1386 – 1396 .
  • Evans , D. J. 2000 . Cyclic and stride reduction methods for generalised tridiagonal matrices . Int. J. Comput. Math , 73 : 487 – 492 .
  • Golub , G. H. and Van Loan , C. F. 1996 . Matrix Computations , 3 , Baltimore , MD : The Johns Hopkins University Press .
  • Heinig , G. 2002 . On the reconstruction of Toeplitz matrix inverses from columns . Linear Algebra Appl , 350 : 199 – 212 .
  • Jiang , Y. L. 2004 . A general approach to waveform relaxation solutions of nonlinear differential-algebraic equations: The continuous-time and discrete-time cases . IEEE Trans. Circuits Systems I-Regular Pap , 51 ( 9 ) : 1770 – 1780 .
  • Karawia , A. A. 2010 . Two algorithms for solving general backward pentadiagonal linear systems . Int. J. Comput. Math , 87 : 2823 – 2830 .
  • Li , J. C. and Jiang , Y. L. 2010 . Generalized tridiagonal preconditioners for solving linear systems . Int. J. Comput. Math , 87 : 3297 – 3310 .
  • Lv , X. G. and Le , J. 2008 . A note on solving nearly penta-diagonal linear systems . Appl. Math. Comput , 204 : 707 – 712 .
  • Melman , A. 2000 . Symmetric centrosymmetric matrix–vector multiplication . Linear Algebra Appl , 320 : 193 – 198 .
  • Navon , I. M. 1987 . PENT: A periodic pentadiagonal systems solver . Commun. Appl. Numer. Methods , 3 : 63 – 69 .
  • Neossi Nguetchue , S. N. and Abelman , S. 2008 . A computational algorithm for solving nearly penta-diagonal linear systems . Appl. Math. Comput , 203 : 629 – 634 .
  • Sogabe , T. 2008 . New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems . Appl. Math. Comput , 202 : 850 – 856 .
  • Yan , W. M. and Chung , K. L. 1994 . A fast algorithm for solving special tridiagonal systems . Computing , 52 : 203 – 211 .

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