Actas de congresos
Affine Arithmetic: Concepts And Applications
Registro en:
Numerical Algorithms. , v. 37, n. 1-4 SPEC. ISS., p. 147 - 158, 2004.
10171398
10.1023/B:NUMA.0000049462.70970.b6
2-s2.0-10044296444
Autor
De Figueiredo L.H.
Stolfi J.
Institución
Resumen
Affine arithmetic is a model for self-validated numerical computation that keeps track of first-order correlations between computed and input quantities. We explain the main concepts in affine arithmetic and how it handles the dependency problem in standard interval arithmetic. We also describe some of its applications. 37 1-4 SPEC. ISS. 147 158 Berz, M., Hoffstätter, G., Computation and application of Taylor polynomials with interval remainder bounds (1998) Reliable Comput., 4 (1), pp. 83-97 De Cusatis Jr., A., De Figueiredo, L.H., Gattass, M., Interval methods for ray casting implicit surfaces with affine arithmetic (1999) Proc. of SIBGRAPI'99, pp. 65-71 De Figueiredo, L.H., Surface intersection using affine arithmetic (1996) Proc. of Graphics Interface'96, pp. 168-175 De Figueiredo, L.H., Stolfi, J., Adaptive enumeration of implicit surfaces with affine arithmetic (1996) Comput. Graphics Forum, 15 (5), pp. 287-296 De Figueiredo, L.H., Stolfi, J., Velho, L., Approximating parametric curves with strip trees using affine arithmetic (2002) Proc. of SIBGRAPI 2002, pp. 163-170 Hansen, E., A generalized interval arithmetic (1975) Lecture Notes in Computer Science, 29, pp. 7-18. , Interval Mathematics, ed. K. Nickel, Springer, New York Heidrich, W., Seidel, H.-P., Ray-tracing procedural displacement shaders (1998) Proc. of Graphics Interface'98, pp. 8-16 Heidrich, W., Slusallek, P., Seidel, H.-P., Sampling procedural shaders using affine arithmetic (1998) ACM Trans. Graphics, 17 (3), pp. 158-176 Stolfi, J., De Figueiredo, L.H., Self-Validated Numerical Methods and Applications (1997) Monograph for 21st Brazilian Mathematics Colloquium, , ftp://ftp.tecgraf.puc-rio.br/pub/lhf/doc/cbm97.ps.gz, IMPA, Rio de Janeiro Tupper, J.A., Graphing Equations with Generalized Interval Arithmetic, , http://www.dgp.utoronto.ca/people/mooncake/msc.html, Master's thesis, Graduate Department of Computer Science, University of Toronto Ziegler, G.M., Lectures on Polytopes (1995) Graduate Texts in Mathematics, 152. , Springer, New York