## Searching for solutions of finite nonlinear systems: an interval approach |

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### Contents

THE ITERATIVE METHOD | 41 |

THE SEARCH PROCEDURE | 55 |

IMPLEMENTATION OF THE SEARCH PROCEDURE | 89 |

2 other sections not shown

### Common terms and phrases

Algorithm 3.1 analyzed beginning with X(O bisection rules CALL computationally verifiable sufficient COND conditions in INCL(X contains no solution convergence coordinate direction current partition EXCL(X exists finite number fixed point FORMAT FORTRAN go to Step half-region selection IIn(Rn integer interval analysis interval arithmetic operation interval number interval vector iterative method Jacobian Lemma Let f,n Lipschitz-continuous m(Xj matrix maximum width rule midpoint Moore n-cube n-dimensional rectangular region natural interval extension NDIR nested sequence nonlinear systems nonsingular number of bisections ordinary Newton's method Otherwise continue PRINT Proof rational function real-valued region for Algorithm region for analysis region selection region X result rule selection safe starting region SAFESTART algorithm search procedure selected for analysis sequence of intervals singular matrix SOLN solution of f(x solvable problem solve f,n stack subroutine suitable initial approximation symmetric interval TEMP Theorem 2.1 verifiable sufficient conditions YF(J Yf(y zero of f