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Original Articles

A modification of krawczyk's algorithm

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Pages 67-77 | Received 02 Apr 1996, Published online: 19 Mar 2007

References

  • Moore , R. E. 1966 . Interval Analysis , Prentice-Hall Inc .
  • Moore , R. E. 1978 . Bounding sets in function spaces with applications to nonlinear operator equations . SIAM Reviews , 20 : 492 – 512 .
  • Moore , R. E. 1977 . safe starting regions for iterative methods . SIAM J. Numer. Anal. , 14 : 1051 – 1065 .
  • Moore , R. E. 1978 . A test for existance of solutions to nonlinear systems . SIAM J. Numer. Anal. , 14 : 611 – 615 .
  • Moore , R. E. 1980 . Interval Methods for nonlinear systems . Computing Supplement , 2 : 113 – 120 .
  • Moore , R. E. 1978 . The contraction mapping fixed point theorem in interval analysis of iterative methods in nonlinear systems . SIAM J. Numer. Anal. , 6 : 1194 – 1196 .
  • Nickel K. On the newton's method in interval arithmatic MRC TSR # 1136 1971
  • Nickel , K. 1967 . Die vollautomatische berechnung einer einfachen nullstellen von f(x) = 0 einschliesslich einer fahlerabschaet zung . Comp. , 2 : 232 – 245 .
  • Madsen , K. 1973 . On the solution of nonlinear equations in interval arithmatic . BIT , 13 : 428 – 433 .
  • Rokne , J. and Lancaster , P. 1969 . Automatic error bounds for the approximate solutions of equations . Comp., , 4 : 294 – 303 .
  • Hansen , E. 1968 . systems of equations using interval arithmatic . Math. Comp. , 22 : 374 – 378 .
  • Hansen , E. 1978 . Interval forms of newton's method . Comp. , 20 : 153 – 163 .
  • Hansen , E. 1981 . Bounding solutions of systems of equations using interval arithmatic . BIT , 21 : 203 – 211 .
  • Alefeld , G. Eine modifikation des newtonverfahren zue bestimmung der reelen nullstellen einer reelen function . ZAMM , 50 T32 – T33 .
  • Alefeld , G. 1974 . Quadratisch konvergente einschliesung von loesungen nichtkonvexer gleichungs systeme . ZAMM , 54 : 335 – 342 .
  • Herzberger , J. 1972 . Ueber die nullstellen bestimmung bei nacherungsweise berechnnente functionen . Comp. , 10 : 23 – 31 .
  • Herzberger , J. 1971 . Zur konvergenz intervall maessiger iterations verfahren . ZAMM , 51 : T56 – T56 .
  • Alefeld , G. and Herzberger , J. 1970 . Verfahren das Newtonverfahren bei nichtlinearen gleichungssystems . ZAMM , 50 : 773 – 774 .
  • Alefeld , G. and Herzberger , J. 1973 . Nullstelleneichliesung mit dem Newton-verfahren ohne invertierung von intervallmatrizen . Num. Math. , 19 : 56 – 64 .
  • Alefeld G. Herzberger J. Einfuegrung in die intervall-rechnung, herausj 1974 Boehling, K. H., Kulisch, V. and Maurer, H. Bibliographisches institut manheim/wien/Zurich.
  • Krawczyk , R. 1969 . Newton-Algorithimen zur bestimmung von nullstellen mit fehberschranken . Comp. , 4 : 187 – 201 .
  • Krawczyk , R. 1970 . Einschliessung von nullstellen mit hilfe einer intervallarithmatic . Comp. , 5 : 356 – 370 .
  • Krawczyk , R. 1984 . Interval iterations for including a set of solutions . Comp. , 32 : 13 – 31 .
  • Krawczyk , R. 1986 . An improved interval newton operator . J. Math. Anal. Appl , 1 : 194 – 207 .
  • Krawczyk , R. 1986 . A class of interval newton operators . Comp. , 37 : 179 – 183 .

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