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pro vyhledávání: '"PAN, VICTOR Y."'
We approximate the d complex zeros of a univariate polynomial p(x) of a degree d or those zeros that lie in a fixed region of interest on the complex plane such as a disc or a square. Our divide and conquer algorithm of STOC 1995 supports solution of
Externí odkaz:
http://arxiv.org/abs/2301.11268
Autor:
Imbach, Rémi, Pan, Victor Y.
In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evaluation, we present sub-algorithms allowing substantial acceleration of
Externí odkaz:
http://arxiv.org/abs/2206.08622
Autor:
Pan, Victor Y.
The DLG root-squaring iterations, due to Dandelin 1826 and rediscovered by Lobachevsky 1834 and Graeffe 1837, have been the main approach to root-finding for a univariate polynomial p(x) in the 19th century and beyond, but not so nowadays because the
Externí odkaz:
http://arxiv.org/abs/2206.01727
Publikováno v:
In Theoretical Computer Science 19 February 2025 1027
Autor:
Imbach, Rémi, Pan, Victor Y.
We depart from our approximation of 2000 of all root radii of a polynomial, which has readily extended Sch{\"o}nhage's efficient algorithm of 1982 for a single root radius. We revisit this extension, advance it, based on our simple but novel idea, an
Externí odkaz:
http://arxiv.org/abs/2102.10821
Autor:
Imbach, Rémi, Pan, Victor Y.
We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial $p$ of degree $d$ with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for multiple roots
Externí odkaz:
http://arxiv.org/abs/1911.06706
A matrix algorithm runs at {\em sublinear cost} if it uses much fewer memory cells and arithmetic operations than the input matrix has entries. Such algorithms are indispensable for Big Data Mining and Analysis. Quite typically in that area the input
Externí odkaz:
http://arxiv.org/abs/1907.10481
Autor:
Imbach, Rémi, Pan, Victor Y.
We seek complex roots of a univariate polynomial $P$ with real or complex coefficients. We address this problem based on recent algorithms that use subdivision and have a nearly optimal complexity. They are particularly efficient when only roots in a
Externí odkaz:
http://arxiv.org/abs/1906.04920
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with LRA at sublinear cost, that is, by using much fewer memory cells and flops th
Externí odkaz:
http://arxiv.org/abs/1906.04112