LEADER 02872nam 2200565 a 450 001 9910483808603321 005 20200520144314.0 010 $a3-540-77851-9 024 7 $a10.1007/978-3-540-77851-6 035 $a(CKB)1000000000437239 035 $a(SSID)ssj0000319463 035 $a(PQKBManifestationID)11230368 035 $a(PQKBTitleCode)TC0000319463 035 $a(PQKBWorkID)10339717 035 $a(PQKB)11098646 035 $a(DE-He213)978-3-540-77851-6 035 $a(MiAaPQ)EBC3068733 035 $a(PPN)12704888X 035 $a(EXLCZ)991000000000437239 100 $a20080122d2008 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPoint estimation of root finding methods /$fMiodrag Petkovic 205 $a1st ed. 2008. 210 $aBerlin $cSpringer$d2008 215 $axii, 210 p. $cill 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v1933 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-77850-0 320 $aIncludes bibliographical references (p. 197-204) and index. 327 $aBasic Concepts -- Iterative Processes and Point Estimation Theory -- Point Estimation of Simultaneous Methods -- Families of Simultaneous Methods of Higher Order: Part I -- Families of Simultaneous Methods of Higher Order: Part II. 330 $aThis book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1933. 606 $aFix-point estimation 606 $aEquations, Roots of 615 0$aFix-point estimation. 615 0$aEquations, Roots of. 676 $a518 686 $a65H05$2msc 700 $aPetkovic$b Miodrag$058168 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483808603321 996 $aPoint estimation of root finding methods$9720013 997 $aUNINA