The complexity of class polynomial computation via floating point approximations
نویسندگان
چکیده
منابع مشابه
The complexity of class polynomial computation via floating point approximations
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton ...
متن کاملThe Complexity of Accurate Floating Point Computation
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational expressions as entries. More precisely, accuracy means the relative error in the output must be less than one (no matter how tiny the output is), and efficiency means...
متن کاملFloating-Point L-Approximations
Computing good polynomial approximations to usual functions is an important topic for the computer evaluation of those functions. These approximations can be good under several criteria, the most desirable being probably that the relative error is as small as possible in the L sense, i.e. everywhere on the interval under study. In the present paper, we investigate a simpler criterion, the L cas...
متن کاملOn the Complexity of Genuinely Polynomial Computation
We present separation results on genuinely (or strongly) time bounded sequential, parallel and non-deterministic complexity classes deened by RAMs with xed set of arithmetic operations. In particular, we separate non-uniform polynomial time from non-uniform parallel polynomial time for the set of operations f+; ?; g (answering a question of M 88]), and uniform deterministic polynomial time from...
متن کاملAccurate Polynomial Evaluation in Floating Point Arithmetic
One of the three main processes associated with polynomials is evaluation; the two other ones being interpolation and root finding. Higham [1, chap. 5] devotes an entire chapter to polynomials and more especially to polynomial evaluation. The small backward error the Horner scheme introduce when evaluated in floating point arithmetic justifies its practical interest. It is well known that the c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-08-02200-x