T. Boult and K. Sikorski, An optimal complexity algorithm for computing the topological degree in two dimensions, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 686698. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On the Complexity of Isolating Real Roots and Computing with.. - Mourrain, al. (2002) (2 citations) (Correct)
.... applications involve the use of various fixed point theorems which can be provided by means of topological degree [9, 33, 60 62, 65] Since Stenger s remarkable and pioneering work [50] many approaches have been developed and studied to compute the topological degree of a function (see, e.g. [1, 5, 6, 22, 23, 27, 51 54, 64, 68, 70]) Stenger s method expresses the topological degree of a continuous mapping F n = f 1 , f n ) defined on a bounded domain D n in R as a constant times a sum of determinants of various nn matrices. The value of the topological degree gives information about the existence of a ....
....be sure that the value of topological degree is given correctly. On the other hand, if moduli of continuity are known (see [54] one can use a deterministic termination criterion in order to obtain the degree with certainty. To this end, Boult and Sikorski proposed in their interesting paper [6] an optimal complexity algorithm for computing with certainty the topological degree for any function from a class F. This class consists of functions F 2 : BQ R defined on the unit square B, which satisfy the Lipschitz condition with constant K 0and whose infinity norm along the boundary of B ....
[Article contains additional citation context not shown here]
T. Boult and K. Sikorski, An optimal complexity algorithm for computing the topological degree in two dimensions, SIAM J. Sci. Statist. Comput. 10 (1989), 686--698.
On the Complexity of Isolating Real Roots and.. - Mourrain, Vrahatis.. (2002) (2 citations) (Correct)
.... applications involve the use of various fixed point theorems which can be provided by means of topological degree [9, 33, 60 62, 65] Since Stenger s remarkable and pioneering work [50] many approaches have been developed and studied to compute the topological degree of a function (see e.g. [1, 5, 6, 22, 23, 27, 51 54, 64, 68, 70]) Stenger s method expresses the topological degree of a continuous mapping F n = f 1 , f n ) defined on a bounded domain n in R as a constant times a sum of determinants of various nn matrices. The value of the topological degree gives information about the existence of ....
....be sure that the value of topological degree is given correctly. On the other hand, if moduli of continuity are known (see [54] one can use a deterministic termination criterion in order to obtain the degree with certainty. To this end, Boult and Sikorski proposed in their interesting paper [6] an optimal complexity algorithm for computing with certainty the topological degree for any function from a class This class consists of functions F 2 : defined on the unit square B, which satisfy the Lipschitz condition with constant K 0 and whose infinity norm along the boundary ....
[Article contains additional citation context not shown here]
T. Boult and K. Sikorski, An optimal complexity algorithm for computing the topological degree in two dimensions, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 686--698.
Sign Methods for Counting and Computing Real Roots of.. - Emiris, Mourrain.. (1999) (Correct)
....polynomials on the domain boundary and of the respective Lipschitz constants on the entire domain. These norms and constants may be bounded either by analytic formulae, interval analysis or the method of section 5. These are recurrent and deep problems in topological degree estimation, see e.g. [1]) so we do not pretend to ooeer original nal solutions. However, we expect that our methods will be eOEcient enough in practice. INRIA Sign methods for computing real roots of algebraic systems 7 5 Sign determination of algebraic expressions The complexity of sign computation for root counting ....
T. Boult and K. Sikorski, An optimal complexity algorithm for computing the topological degree in two dimensions, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 686698. INRIA Sign methods for computing real roots of algebraic systems 9
Isolation of Real Roots and Computation of the Topological Degree - Mourrain, al. (2001) (Correct)
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T. Boult and K. Sikorski, An optimal complexity algorithm for computing the topological degree in two dimensions, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 686698.
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