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JC
2006
13 years 7 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
13 years 7 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
13 years 7 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
13 years 7 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
13 years 7 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...