Jonathan Ashley, Brian Marcus, et al.
Ergodic Theory and Dynamical Systems
Certain questions concerning the arithmetic complexity of univariate polynomial evaluation are considered. The principal technical results show that there exist polynomials f,g, and h with h = fg, such that h requires substantially fewer arithmetic operations than either f or g. However, if the coefficients of f are algebraically independent, then any h = fg is as hard to evaluate as f. The question of the relative complexities of f and fg is viewed as a special case of the following question: given an operator Δ which maps polynomials to sets of polynomials, what savings in arithmetic operations is achievable by evaluating some polynomial h ε{lunate} Δ(f) rather than f? Observations and open questions concerning several operators are discussed. © 1978.
Jonathan Ashley, Brian Marcus, et al.
Ergodic Theory and Dynamical Systems
Igor Devetak, Andreas Winter
ISIT 2003
Alfred K. Wong, Antoinette F. Molless, et al.
SPIE Advanced Lithography 2000
Imran Nasim, Michael E. Henderson
Mathematics