We investigate the complexity of (1) computing the characteristic polynomial, the minimal polynomial, and all the invariant factors of an integer matrix, and of (2) verifying them, when the coefficients are given as input. It is known that each coefficient of the characteristic polynomial of a...
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a functio...
The order of the polynomial function determines its complexity and accuracy. Basis functions are successively added to the model until all response points are interpolated. The method favours low-degree terms over higher-degree terms. Nevertheless, the method can choose higher-degree terms depending ...
• What is the complexity of computing the smallest annihilating polynomial of a given set of algebraically dependent polynomials? For the sake of concreteness, we shall fix the underlying field F to be the field Q of rational numbers. The questions posed above make sense for any field and ...
We introduce a new and natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits...
Although polynomial-time complexity theory has been formulated in terms of decision problems, polynomial-time decision algorithms generally operate by attempting to construct a solution to an optimization version of the problem at hand. Thus it is that self-reducibility, the process by which a decisio...
Non-intrusive polynomial chaos expansion Assume a probability space , where Ω is an event space, is a σ-algebra on Ω and is a probability measure on . If the Doob-Dynkin lemma is satisfied and the input variable of a mathematical model, , is a random variable , the model response is...
Algorithms with polynomial complexity for determining the stability of nondeterministic discrete-event systems判定非确定离散事件系统稳定性的多项式复杂度算法非确定自动机/形式语言模型稳定性梯度搜索多项式复杂度离散事件系统观测器搜索算法拟距离节点状态判定算法...
Since all the bounds on time complexity given in the present paper are only specified up to a polynomial, while on the other hand all reasonable models of computation (such as Taring machines or RAM's) are equivalent in the sense of polynomial time complexity, the choice of a particular ...
Approximation Complexity for Piecewise Monotone Functions Real Data Brooks, M.: Approximation complexity for piecewise monotone functions and real data. Computers and Mathematics with Applications 27 (1994)... M Brooks - 《Computers & Mathematics with Applications》 被引量: 13发表: 1994年 Non-similari...