Real algebraic number computation using interval arithmetic
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Polynomial real root isolation using approximate arithmetic
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Remarks on automatic algorithm stabilization
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Minimum converging precision of the QR-factorization algorithm for real polynomial GCD
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A new Gröbner basis conversion method based on stabilization techniques
Theoretical Computer Science
Structures of precision losses in computing approximate Gröbner bases
Journal of Symbolic Computation
Hi-index | 0.00 |
For a certain class of algebraic algorithms, we propose a new method that reduces the number of exact computational steps needed for obtaining exact results. This method is the floating-point interval method using zero rewriting and symbols. Zero rewriting, which is from stabilization techniques, rewrites an interval coefficient into the zero interval if the interval contains zero. Symbols are used to keep track of the execution path of the original algorithm with exact computations, so that the associated real coefficients can be computed by evaluating the symbols. The key point is that at each stage of zero rewriting, one checks to see if the zero rewriting is really correct by exploiting the associated symbol. This method mostly uses floating-point computations; the exact computations are only performed at the stage of zero rewriting and in the final evaluation to get the exact coefficients. Moreover, one does not need to check the correctness of the output.