Solving systems of linear Boolean equations with noisy right-hand sides over the reals
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Evgeny K. Alekseev
,
Igor’ B. Oshkin
Abstract
The paper is concerned with the problem of solution of a system of linear equations with noisy right-hand side in the following setting: one knows a random m × N-matrix A with entries from {–1, 1} and a vector xA + ξ ∈ ℝN, where ξ is the noise vector from ℝN, whose entries are independent realizations of a normally distributed random variable with parameters 0 and σ2, and x is a random vector with coordinates from {–1, 1}. The sought-for parameter is the vector x. We propose a method for constructing a set containing the sought-for vector with probability not smaller than the given one and estimate the cardinality of this set. Theoretical calculations of the parameters of the method are illustrated by experiments demonstrating the practical implementability of the method for cases when direct enumeration of all possible values of x is unfeasible.
Originally published in Diskretnaya Matematika (2017) 29, №1, 3–9 (in Russian).
Acknowledgement
The authors are grateful to Andrey V. Ivanov for valuable comments, constructive criticism, and his interest in this research.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Solving systems of linear Boolean equations with noisy right-hand sides over the reals
- Reduced multitype critical branching processes in random environment
- On automorphisms of a distance-regular graph with intersection array {99, 84, 30; 1, 6, 54}
- On the best choice of a branching variable in the subset sum problem
- On periodic properties of polylinear shift registers
- Upper estimate of a combinatorial sum
Articles in the same Issue
- Frontmatter
- Solving systems of linear Boolean equations with noisy right-hand sides over the reals
- Reduced multitype critical branching processes in random environment
- On automorphisms of a distance-regular graph with intersection array {99, 84, 30; 1, 6, 54}
- On the best choice of a branching variable in the subset sum problem
- On periodic properties of polylinear shift registers
- Upper estimate of a combinatorial sum
