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On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as JVP-complete… Expand
A Simple Unpredictable Pseudo-Random Number Generator
TLDR
Global Stability of Dynamical Systems
- M. Shub
- Mathematics
- 22 December 1986
1 Generalities.- 2 Filtrations.- 3 Sequences of Filtrations.- 4 Hyperbolic Sets.- 5 Stable Manifolds.- 6 Stable Manifolds for Hyperbolic Sets.- 7 More Consequences of Hyperbolicity.- 8 Stability.- 9… Expand
Complexity of Bezout’s Theorem II Volumes and Probabilities
In this paper we study volume estimates in the space of systems of n homegeneous polynomial equations of fixed degrees d i with respect to a natural Hermitian structure on the space of such systems… Expand
How many eigenvalues of a random matrix are real
- A. Edelman, E. Kostlan, M. Shub
- Mathematics
- 1994
Let A be an n x n matrix whose elements are independent random variables with standard normal distributions. As n oo , the expected number of real eigenvalues is asymptotic to V/7r . We obtain a… Expand
Complexity of Bezout's theorem IV: probability of success; extensions
We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of n homogeneous polynomial equations in $n + 1$ complex variables of fixed degrees… Expand
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