A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously
In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. We present a new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions. Our result is obtained by combini...
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| Veröffentlicht in: | Journal of Complexity 2014-06, Vol.30 (3), p.366-380 |
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| container_title | Journal of Complexity |
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| creator | Proinov, Petko D. Petkova, Milena D. |
| description | In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. We present a new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions. Our result is obtained by combining ideas of Weierstrass (1891) and Proinov (2010). A priori and a posteriori error estimates are also provided under the new initial conditions. |
| doi_str_mv | 10.1016/j.jco.2013.11.002 |
| format | Article |
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A priori and a posteriori error estimates are also provided under the new initial conditions.</description><subject>Approximation</subject><subject>Convergence</subject><subject>Error estimates</subject><subject>Errors</subject><subject>Estimates</subject><subject>Initial conditions</subject><subject>Mathematical analysis</subject><subject>Normed fields</subject><subject>Polynomial zeros</subject><subject>Polynomials</subject><subject>Semilocal convergence</subject><subject>Simultaneous methods</subject><subject>Theorems</subject><subject>Weierstrass method</subject><issn>0885-064X</issn><issn>1090-2708</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kEtPwzAQhC0EEqXwA7j5yCVhN--IU1XxkipxAcHNcpx16yqJi50WlV-PSzlz2pV2ZjT7MXaNECNgcbuO18rGCWAaI8YAyQmbINQQJSVUp2wCVZVHUGQf5-zC-zUAYl7ghNkZH-iLe-pNZ5XsuLLDjtySBkV8XJF11HNt3WHn72TI-dFJ73lP48q2vydthtYMS_5NznpuNZd8Y7v9YHsTAr3pt90oB7Jb3-0v2ZmWnaervzllbw_3r_OnaPHy-DyfLSKVlukYZUVdaczrRNZ5U-oWZCarpM6hAWp0Sa2GLNNU1RKbrEgbKtO2abIkAUrKqsV0ym6OuRtnP7fkR9Ebr6jrjkUE5mngVuZQBikepSrU94602DjTS7cXCOIAV6xFgCsOcAWiCHCD5-7oofDDLlARXpkDs9Y4UqNorfnH_QNnF4RX</recordid><startdate>20140601</startdate><enddate>20140601</enddate><creator>Proinov, Petko D.</creator><creator>Petkova, Milena D.</creator><general>Elsevier Inc</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20140601</creationdate><title>A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously</title><author>Proinov, Petko D. ; Petkova, Milena D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-4698f1592a95b7fd0a4a82950b0ebf7edf044fe89a1b463be73dbb4220e278d13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Approximation</topic><topic>Convergence</topic><topic>Error estimates</topic><topic>Errors</topic><topic>Estimates</topic><topic>Initial conditions</topic><topic>Mathematical analysis</topic><topic>Normed fields</topic><topic>Polynomial zeros</topic><topic>Polynomials</topic><topic>Semilocal convergence</topic><topic>Simultaneous methods</topic><topic>Theorems</topic><topic>Weierstrass method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Proinov, Petko D.</creatorcontrib><creatorcontrib>Petkova, Milena D.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of Complexity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Proinov, Petko D.</au><au>Petkova, Milena D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously</atitle><jtitle>Journal of Complexity</jtitle><date>2014-06-01</date><risdate>2014</risdate><volume>30</volume><issue>3</issue><spage>366</spage><epage>380</epage><pages>366-380</pages><issn>0885-064X</issn><eissn>1090-2708</eissn><abstract>In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. 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| ispartof | Journal of Complexity, 2014-06, Vol.30 (3), p.366-380 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Approximation Convergence Error estimates Errors Estimates Initial conditions Mathematical analysis Normed fields Polynomial zeros Polynomials Semilocal convergence Simultaneous methods Theorems Weierstrass method |
| title | A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously |
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