Polynomial decomposition algorithms

Polynomial Decomposition Algorithms

We examine the question of when a polynomial f over a commutative ring has a nontrivial functional decomposition f = g ◦ h. Previous algorithms [2, 3, 1] are exponential-time in the worst case, require polynomial factorization, and only work over fields of characteristic 0. We present an O(n2)-time algorithm. We also show that the problem is in NC . The algorithm does not use polynomial factori...

General Polynomial Time Decomposition Algorithms

We present a general decomposition algorithm that is uniformly applicable to every (suitably normalized) instance of Convex Quadratic Optimization and efficiently approaches an optimal solution. The number of iterations required to be within ε of optimality grows linearly with 1/ε and quadratically with the number m of variables. The working set selection can be performed in polynomial time. If...

پیشنهاد روش جدیدی برای محاسبه polynomial singular value decomposition ) psvd )

در این پایان نامه به معرفی روشهای مختلف محاسبه psvd می پردازیم. بخشی از این روشها به بررسی روشهای مختلف محاسبه psvd در مقالات مطالعه شده می پردازد که می توان به محاسبهpsvd با استفاده از الگوریتمهای pqrd و pevd و sbr2 و محاسبه psvd براساس تکنیک kogbetliantz و روش پارامتریک برای محاسبه psvd اشاره نمود. بخش بعدی نیز به بررسی روشهای مستقیم پیشنهادی محاسبه psvd برای ماتریسهای 2×2و2× n و n×2 و 3× n و...

Algorithms for computing triangular decomposition of polynomial systems

We discuss algorithmic advances which have extended the pioneer work of Wu on triangular decompositions. We start with an overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory. We then present new techniques that we regard as essential to the recent success and for future research directions in the development of t...

Biconjugate Decomposition Using ABS Algorithms