Some properties of zeros of polynomials with vanishing coefficients Export

@article{citeulike:4163247, abstract = {It is well-known that when a polynomial whose coefficients are continuous functions of a parameter loses its degree then some of its zeros must vanish at infinity . In this paper, we consider such a situation: we examine how roots of a complex polynomial tend to infinity as some of its coefficients, including the leading one, tend to zero. We show, among other things, that in such a situation the unbounded paths traced by the roots of the polynomial have asymptotes; we also obtain their formulas. Some examples are presented to complete and illustrate the results.}, author = {Bia{\l}as, Stanis{\l}aw and G\'{o}ra, Micha{\l}}, citeulike-article-id = {4163247}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.laa.2008.11.008}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0024379508005387}, day = {15}, doi = {10.1016/j.laa.2008.11.008}, issn = {00243795}, journal = {Linear Algebra and its Applications}, keywords = {complex\_analysis, confluence, root\_location, univariate\_functions}, month = {April}, number = {8-9}, pages = {1976--1991}, posted-at = {2009-03-10 21:38:01}, priority = {2}, title = {Some properties of zeros of polynomials with vanishing coefficients}, url = {http://dx.doi.org/10.1016/j.laa.2008.11.008}, volume = {430}, year = {2009} }

TY - JOUR ID - citeulike:4163247 L3 - citeulike-article-id:4163247 N2 - It is well-known that when a polynomial whose coefficients are continuous functions of a parameter loses its degree then some of its zeros must vanish at infinity . In this paper, we consider such a situation: we examine how roots of a complex polynomial tend to infinity as some of its coefficients, including the leading one, tend to zero. We show, among other things, that in such a situation the unbounded paths traced by the roots of the polynomial have asymptotes; we also obtain their formulas. Some examples are presented to complete and illustrate the results. IS - 8-9 JF - Linear Algebra and its Applications SN - 00243795 EP - 1991 TI - Some properties of zeros of polynomials with vanishing coefficients VL - 430 SP - 1976 KW - complex_analysis KW - confluence KW - root_location KW - univariate_functions AU - Białas, Stanisław AU - Góra, Michał PY - 2009/04/15/ UR - http://dx.doi.org/10.1016/j.laa.2008.11.008 ER -