{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:38Z","timestamp":1753881218967,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,10,3]],"date-time":"2012-10-03T00:00:00Z","timestamp":1349222400000},"content-version":"vor","delay-in-days":276,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100005417","name":"Universiti Teknologi Malaysia","doi-asserted-by":"publisher","award":["Q.J130000.7126.04J05"],"award-info":[{"award-number":["Q.J130000.7126.04J05"]}],"id":[{"id":"10.13039\/501100005417","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>In all polynomial zerofinding algorithms, a good convergence requires a very good initial approximation of the exact roots. The objective of the work is to study the conditions for determining the initial approximations for an iterative matrix zerofinding method. The investigation is based on the Newbery\u2032s matrix construction which is similar to Fiedler\u2032s construction associated with a characteristic polynomial. To ensure that convergence to both the real and complex roots of polynomials can be attained, three methods are employed. It is found that the initial values for the Fiedler\u2032s companion matrix which is supplied by the Schmeisser\u2032s method give a better approximation to the solution in comparison to when working on these values using the Schmeisser\u2032s construction towards finding the solutions. In addition, empirical results suggest that a good convergence can still be attained when an initial approximation for the polynomial root is selected away from its real value while other approximations should be sufficiently close to their real values. Tables and figures on the errors that resulted from the implementation of the method are also given.<\/jats:p>","DOI":"10.1155\/2012\/167927","type":"journal-article","created":{"date-parts":[[2012,10,3]],"date-time":"2012-10-03T21:03:25Z","timestamp":1349298205000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Choosing Improved Initial Values for Polynomial Zerofinding in Extended Newbery Method to Obtain Convergence"],"prefix":"10.1155","volume":"2012","author":[{"given":"Saeid","family":"Saidanlu","sequence":"first","affiliation":[]},{"given":"Nor\u2019aini","family":"Aris","sequence":"additional","affiliation":[]},{"given":"Ali","family":"Abd Rahman","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,3]]},"reference":[{"volume-title":"Rounding Errors in Algebraic Processes","year":"1963","author":"Wilkinson J. H.","key":"e_1_2_11_1_2"},{"volume-title":"The Algebraic Eigenvalue Problem","year":"1965","author":"Wilkinson J. H.","key":"e_1_2_11_2_2"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0718069"},{"key":"e_1_2_11_4_2","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1007\/BF02163334","article-title":"A three-stage variable-shift iteration for polynomial zeros and its relation to generalized rayleigh iteration","volume":"14","author":"Jenkins M. A.","year":"1970","journal-title":"Numerische Mathematik"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/361254.361262"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933450"},{"key":"e_1_2_11_7_2","unstructured":"TohK. C.andTrefethenL. N. Pseudozeros of Polynomial and Pseudo spectra of companion matrices Technical Report 1993 no. TR 93-1360 Department of Computer Science Cornell University Ithaca NY USA."},{"key":"e_1_2_11_8_2","unstructured":"MadsenK.andReidJ. Fortran subroutines for finding polynomial zeros 1975 no. HL.75\/1172(C.13) Computer Science and Systems Division A.E.R.E. Harwell UK."},{"volume-title":"The Mathematical Basis for a New Polynomial Rootfinder with Quadratic Convergence","year":"1993","author":"Hull T. E.","key":"e_1_2_11_9_2"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2005.07.018"},{"key":"e_1_2_11_11_2","series-title":"Lecture Notes for a Summer School","volume-title":"Polynomial Roots and Approximate Greatest Common Divisors","author":"Winkler J. R.","year":"2007"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-04-01692-8"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(94)00202-V"},{"key":"e_1_2_11_14_2","article-title":"A family of test matrices","volume":"7","author":"Newbery A. C. R.","year":"1964","journal-title":"Communications of the Association for Computing Machinery"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90323-5"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90268-S"},{"key":"e_1_2_11_17_2","first-page":"4","article-title":"Numerical solution of algebraic equations which have roots with almost the same modulus","volume":"1","author":"Fiedler M.","year":"1956","journal-title":"Aplikace Matematiky"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/167927.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/167927.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/167927","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:11:06Z","timestamp":1718089866000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/167927"}},"subtitle":[],"editor":[{"given":"Ram N.","family":"Mohapatra","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/167927"],"URL":"https:\/\/doi.org\/10.1155\/2012\/167927","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-04-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-08-19","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-10-03","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"167927"}}