T. Thiele, 1993. Personal Communication. 17 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Efficient Perturbations for Handling Geometric Degeneracies - Emiris, Canny, Seidel (1994) (7 citations) (Correct)
....P d j=1 i 2j d 2 3 7 7 7 7 5 ; which follows from Proposition 10 or Theorem 11. Unfortunately, the hypothesis of the theorem is not readily satisfied by the second perturbation (4) A similar scheme, with residues taken mod q, with q = Omega (n d Gamma1 ) has been recently shown [30] to be valid, offering a slight improvement on complexity. The perturbed determinant expands to the sum det Gamma d 2 (ffl) fi fi fi fi fi fi fi fi 1 x i 1 ;1 (ffl) x i 1 ;d (ffl) ffl 2 P d j=1 i 2j 1 ffl(2 P d j=1 x i 1 ;j i j 1 Gamma i d 2 1 ) ....
T. Thiele, 1993. Personal Communication. 17
Efficient Perturbations for Handling Geometric Degeneracies - Emiris, Canny, Seidel (1997) (7 citations) (Correct)
....i d d 2 P d j=1 i 2j d 2 3 7 7 7 7 5 ; which follows from Proposition 10 or Theorem 11. Unfortunately, the hypothesis of the theorem is not readily satisfied by the second perturbation (5) A similar scheme, with residues taken mod q, with q = Omega (n d Gamma1 ) has been recently shown [27] to be valid, offering a slight improvement on complexity. For the first scheme, the perturbed determinant expands to det Gamma d 2 (ffl) fi fi fi fi fi fi fi fi 1 x i 1 ;1 (ffl) x i 1 ;d (ffl) ffl 2 P d j=1 i 2j 1 ffl(2 P d j=1 x i 1 ;j i j 1 Gamma i d 2 1 ) ....
T. Thiele, 1993. Personal Communication.
Sparse Elimination and Applications in Kinematics - Emiris (1994) (10 citations) (Correct)
....P d j=1 i 2j d 2 3 7 7 7 7 5 ; which follows from proposition 6.3.3 or theorem 6.3.4. Unfortunately, the hypothesis of the theorem is not readily satisfied by the second perturbation (6. 4) A similar scheme, with residues taken mod q, with q = Omega (n d Gamma1 ) has been recently shown [Thi93] to be valid, offering a slight improvement on complexity. The perturbed determinant expands to the sum det Gamma d 2 (ffl) fi fi fi fi fi fi fi fi 1 x i 1 ;1 (ffl) x i 1 ;d (ffl) ffl 2 P d j=1 i 2j 1 ffl(2 P d j=1 x i 1 ;j i j 1 Gamma i d 2 1 ) 1 x i ....
T. Thiele, 1993. Personal Communication.
Efficient Perturbations for Handling Geometric Degeneracies - Emiris, Canny, Seidel (1997) (7 citations) (Correct)
....i d d 2 P d j=1 i 2j d 2 3 7 7 7 7 5 ; which follows from Proposition 10 or Theorem 11. Unfortunately, the hypothesis of the theorem is not readily satisfied by the second perturbation (5) A similar scheme, with residues taken mod q, with q = Omega (n d Gamma1 ) has been recently shown [33] to be valid, offering a slight improvement on complexity. The perturbed determinant expands to det Gamma d 2 (ffl) fi fi fi fi fi fi fi fi 1 x i 1 ;1 (ffl) x i 1 ;d (ffl) ffl 2 P d j=1 i 2j 1 ffl(2 P d j=1 x i 1 ;j i j 1 Gamma i d 2 1 ) 1 x i d 2 ;1 ....
T. Thiele, 1993. Personal Communication.
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