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JC
2006
14 years 11 months ago
2006
We give a correspondence between two notions of complexity for real numbers and functions: poly-time computability according to Ko and a notion that arises naturally when one cons...
JC
2000
14 years 11 months ago
2000
The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. In this paper we discuss some basic degr...
JC
2000
14 years 11 months ago
2000
We study the complexity of approximating the Stieltjes integral R 1 0 f(x)dg(x) for functions f having r continuous derivatives and functions g whose sth derivative has bounded va...
JC
2000
14 years 11 months ago
2000
Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a fundamental problem of computational real algebraic geometry. We propose an algorithm ...
JC
2006
14 years 11 months ago
2006
We study the randomized approximation of weakly singular integral operators. For a suitable class of kernels having a standard type of singularity and being otherwise of finite sm...