Showing papers in "Journal of Complexity in 1995"

TL;DR: An upper bound is obtained, which is independent of d, for the number, n(?, d), of points for which discrepancy is at most ?, n (?, d) ? 7.26??2.454, ?d, ? ? 1.

TL;DR: It is NP-hard to determine whether a set of n rational points in d dimensions is affinely or linearly degenerate and an algorithm for approximating ?

TL;DR: The results of information-based complexity, see the book of Traub, Wasilkowski, and Wo?niakowski (1988, "Information-Based Complexity," Academic Press, New York/London), can be reconstructed in this model with only minor changes and two variants of stochastic algorithms are defined.

TL;DR: Issues of structural complexity in a linear version of the Blum-Shub-Smale model of computation over the real numbers and real versions of PSPACE and of the polynomial time hierarchy are investigated.

TL;DR: This inequality is an analog of Talagrand′s inequality for the Haar polynomials and is used to prove some new estimates of the entropy numbers of classes of functions with bounded mixed difference or derivative in the most difficult case of the uniform norm.

TL;DR: This paper studies the approximation of the identity operator and the integral operator Tm by Jackson operators, discreteJackson operators, and spline operators, respectively, on the Wiener space and obtains average error estimation.

TL;DR: An algorithm is proposed for producing the complexification, Zariski closure, and also for finding all irreducible components of W.

TL;DR: It is shown that the problem of finding a similarity transformation G such that G?1AG is block diagonal with the condition number of G being at most ?

TL;DR: As it turns out, a slight modification of the "crude Monte Carlo method" with fixed cardinality is strictly optimal even among possibly nonlinear Monte Carlo rules with varying cardinality.

TL;DR: A subclass PMLF of PDLF is defined and it is shown that the fixed points and the intersection points of polynomial-time computable functions are not polynomially computable ifPMLF contains a function on unary inputs that is not poynomial- time computable.

TL;DR: Using a variational principle for s-numbers, estimates are obtained for the linear, Gel′fand.

TL;DR: It is shown that under the assumption of a certain generalized Riemann hypothesis the problem of verifying the value of the class number of an arbitrary algebraic number field of arbitrary degree belongs to the complexity class NP.

TL;DR: This paper considers the computational complexity of computing winning strategies in diophantine games, where two players take turns choosing natural numbers and the win condition is a polynomial equation in the variables.

TL;DR: For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative the authors prove matching lower and upper hounds in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.

TL;DR: Two termination criteria which are used in computational practice for linear problems in the average case setting are studied and it is proved that the second termination criterion gives satisfactory results for all cases.

TL;DR: Some upper and lower estimates on the diameter of inaccurate information are derived and compared to that of exact information and conditions under which the bounds coincide and yield the diameter exactly are pointed out.

TL;DR: The paper presents an algorithm which achieves the asymptotic rate 1 2 for almost all values of the minimizer x* for functions ƒ smooth at x*.

TL;DR: A lower bound of order n3 is shown for the resultant of quadratic forms for zero in the complex PC versus the NPC problem by focussing on lower bounds on testing the resultant for zero.

TL;DR: This paper proves that comp(?, d) = ?(c(d)(ln 1/?)d), where the ?-constant depends on d, and shows how to construct a finite element p-method that can compute an ?-approximation with cost c(d) so that this finite element method is a nearly optimal complexity algorithm for d-dimensional elliptic problems with analytic data.

TL;DR: The joint density for the singular values of a random complex matrix A uniformly distributed on ||A||F = 1 is derived and is used by Shub and Smale in their analysis of the complexity of Bezout?s theorem.

TL;DR: It is shown that adaptive methods are not (much) better than nonadaptive methods, if the minimal information cost of obtaining approximation with accuracy √ϵ using only non Adaptive methods is an (almost) convex function of ϵ.

TL;DR: A fast method of binary segmentation for multivariate integer polynomials and applies it to polynomial multiplication, pseudodivision, resultant and gcd calculations is developed.

TL;DR: The worst case complexity of operator equations Lu = f where L : G → X is a bounded linear injection of normed linear spaces is studied and the Tricomi problem, the inverse finite Laplace transform, and the backwards heat equation are determined.