LEADER 03769nam 2200637 a 450 001 9910815788303321 005 20200520144314.0 010 $a1-283-25095-0 010 $a9786613250957 010 $a0-8176-4703-1 024 7 $a10.1007/978-0-8176-4703-2 035 $a(CKB)2670000000034238 035 $a(EBL)763634 035 $a(OCoLC)649426328 035 $a(SSID)ssj0000450293 035 $a(PQKBManifestationID)11309083 035 $a(PQKBTitleCode)TC0000450293 035 $a(PQKBWorkID)10434700 035 $a(PQKB)11414904 035 $a(DE-He213)978-0-8176-4703-2 035 $a(MiAaPQ)EBC763634 035 $a(Au-PeEL)EBL763634 035 $a(CaPaEBR)ebr10395445 035 $a(CaONFJC)MIL325095 035 $a(PPN)149040148 035 $a(EXLCZ)992670000000034238 100 $a20071129d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aShape-preserving approximation by real and complex polynomials /$fSorin G. Gal 205 $a1st ed. 2008. 210 $aBoston $cBirkha?user$d2008 215 $a1 online resource (364 pages) 300 $aDescription based upon print version of record. 311 $a0-8176-4702-3 320 $aIncludes bibliographical references and index. 327 $aShape-Preserving Approximation By Real Univariate Polynomials -- Shape-Preserving Approximation by Real Multivariate Polynomials -- Shape-Preserving Approximation by Complex Univariate Polynomials -- Shape-Preserving Approximation by Complex Multivariate Polynomials -- Appendix : Some Related Topics. 330 $aThis monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems that arise in science and engineering and require an optimal mathematical representation of physical reality. The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of real functions of one real variable by real polynomials; shape-preserving approximation of real functions of several real variables by multivariate real polynomials; shape-preserving approximation of analytic functions of one complex variable by complex polynomials in the unit disk; and shape-preserving approximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendix treats related results of non-polynomial and non-spline approximations preserving shape including those by complexified operators with applications to complex partial differential equations. Shape-Preserving Approximation by Real and Complex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students and researchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, chemistry, fluid mechanics, and engineering. 606 $aApproximation theory 606 $aBernstein polynomials 606 $aMultivariate analysis 615 0$aApproximation theory. 615 0$aBernstein polynomials. 615 0$aMultivariate analysis. 676 $a511.4 700 $aGal$b Sorin G.$f1953-$0474332 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910815788303321 996 $aShape-preserving approximation by real and complex polynomials$94040357 997 $aUNINA