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Showing 1 to 5 of 5 for “"Algebraic Complexity"”.
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Polynomial ideals in algebraic complexity
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms
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On The Parallelization Of Integer Polynomial Multiplication
… To achieve this goal, one needs to consider both algebraic complexity and parallelism, plus making efficient use of memory traffic, cache, and reducing overheads in the implementations. Polynomial multiplication is at the core of many algorithms in symbolic computation such as real root isolation …
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Algebraic dependence testing in the perspective of algebraic matroids
We study the computational problem called algebraic dependence testing, where we seek to find a polynomial relation among a set of polynomials. This notion generalizes linear dependence, and understanding it has had applications to deterministic polynomial identity testing and algebraic circuit …
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Upper and Lower Complexity Bounds for Some Problems in Elementary Geometry
… mainly dedicated to the study of upper and lower complexity bounds of some problems in the context of semi-algebraic geometry. We present a brief summary of its contents. In Chapter 1 we analyze the algebraic complexity of the linear programming feasibility problem over the reals and prove …
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On the Fourier decay and the dimension of self-similar measures
… geometry. It is expected that unless there are algebraic obstructions, self-similar measure have full dimension, are absolutely continuous with respect to the Lebesgue measure and have power Fourier decay, meaning that $|\widehat{\mu}(\xi)| \lsim |\xi|^{-\alpha}$ for some $\alpha>0$. While this …