论文信息 - Algebraic Computation, Numerical Computation and Verified Inclusions

Algebraic Computation, Numerical Computation and Verified Inclusions

The three different types of computation — the algebraic manipulation, the numerical computation and the computation of verified results — are aiming on different problems and deliver qualitatively different results, each method having its specific advantages for specific classes of problems. The following remarks give some thoughts on possible combinations of all three methods to obtain algorithms benefitting from the specific strength of either method.

Siegfried M. Rump | S. Rump

[1] Siegfried M. Rump,et al. Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds , 1984 .

[2] Willard L. Miranker,et al. A new approach to scientific computation , 1983 .

[3] Siegfried M. Rump,et al. Solving Algebraic Problems with High Accuracy , 1983, IMACS World Congress.

[4] G. Alefeld,et al. Introduction to Interval Computation , 1983 .

[5] James R. Pinkert. Interval arithmetic applied to polynomial remainder sequences , 1976, SYMSAC '76.

[6] Siegfried M. Rump. On the sign of a real algebraic number , 1976, SYMSAC '76.

[7] Ramon E. Moore. Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[8] Louis B. Rall,et al. Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.

[9] Willard L. Miranker,et al. Computer arithmetic in theory and practice , 1981, Computer science and applied mathematics.

[10] U. Kulisch,et al. Rechnerarithmetik und die Behandlung Algebraischer Probleme , 1986 .