- -

Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

Mostrar el registro completo del ítem

Moreno Flores, J.; Saiz Martinez, A. (2011). Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems. Numerical Algorithms. 58(2):203-233. doi:10.1007/s11075-011-9453-x

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/49340

Ficheros en el ítem

[Cerrado]
Nombre: Moreno;Saiz - Inverse ...
Tamaño: 480.4Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor

Metadatos del ítem

Título: Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems
Autor: Moreno Flores, Joaquín Saiz Martinez, Andrés
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
In this paper we present a new algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial, fP(y). The foundations of the computing of such series have been previously developed ...[+]
Palabras clave: Newton’s method , Quasi-Newton methods , Inverse function of polynomials , Polynomial zeros , Polynomial systems zeros , Algorithms , Nonlinear equations
Derechos de uso: Cerrado
Fuente:
Numerical Algorithms. (issn: 1017-1398 )
DOI: 10.1007/s11075-011-9453-x
Editorial:
Springer Verlag (Germany)
Versión del editor: http://dx.doi.org/10.1007/s11075-011-9453-x
Tipo: Artículo

References

Pérez, R., Rocha, V.L.: Recent applications and numerical implementation of quasi-Newton methods for solving nonlinear systems of equations. Numer. Algorithms 35, 261–285 (2004)

Pan, V.Y.: Solving a polynomial equation: some history and recent progress. SIAM Rev. 39(2), 187–220 (1997)

Pan, V.Y.: On approximating polynomial zeros: modified quad tree (Weyl’s) construction and improved Newton’s iteration. Research Report 2894, INRIA, Sophia-Antipolis, France (1996) [+]
Pérez, R., Rocha, V.L.: Recent applications and numerical implementation of quasi-Newton methods for solving nonlinear systems of equations. Numer. Algorithms 35, 261–285 (2004)

Pan, V.Y.: Solving a polynomial equation: some history and recent progress. SIAM Rev. 39(2), 187–220 (1997)

Pan, V.Y.: On approximating polynomial zeros: modified quad tree (Weyl’s) construction and improved Newton’s iteration. Research Report 2894, INRIA, Sophia-Antipolis, France (1996)

Pan, V.Y.: Optimal and nearly optimal algorithms for approximating polynomial zeros. Comput. Math. Appl. 31, 97–138 (1996)

Mcnamee, J.M.: A bibliography on roots of polynomials. J. Comput. Appl. Math. 47, 391–394 (1993)

Pan, V.Y.: Fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros. Comput. and Math. 17, 1475–1480 (1989)

Davidon, W.C.: Variable metric methods for min imitation. Research and Development Report ANL-5990 Rev (1959)

Broyden, C.G., Luss, D.: A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19, 577–593 (1965)

Ortega, J.M., Reinboldt, W.C.: Iterative Solutions of Nonlinear Equations in Several Variables. Academic Press, New York (1970)

Dennid, J.E., More, J.J.: Quasi-Newton methods, motivations and theory. SIAM Rev. 19, 46–89 (1977)

Martínez, J.M.: Practical quasi-Newton methods for solving nonlinear systems. J. Comput. Appl. Math. 124, 97–121 (2000)

Zhang, J.Z., Chen, L.H., Deng, N.Y.: A family scaled factorized Broyden-like methods for nonlinear least squares problems. SIAM J. Optm. 10(4), 1163–1179 (2000)

Brezinski, C.: Classification of quasi-Newton methods. Numer. Algorithms 33, 123–135 (2003)

Eriksson, J., Gulliksson, M.E.: Local results for the Gauss-Nreyon method on constrained rank-deficient nonlinear least squares. Math. Comput.73(248), 1865–1883 (2003)

Birgin, E.G., Krejic, N., Martínez, J.M.: Globally convergent inexact quasi-Newton methods for solving nonlinear systems. Numer. Algorithms 32, 249–260 (2003)

Yabe, H., Martínez, H.J., Tapia, R.A.: On sizing and shifting the BFGS update within the sized-Broyden family of secant updates. SIAM J. Optim. 15(1), 139–160 (2004)

Heng-Bin, A.: On convergence of the additive archway preconditioned inexact newton method. SIAM J. Numer. Anal. 43(5), 1850–1871 (2005)

Brett, W.B.: Tensor-Krylov methods for solving large-scale systems of nonlinear equations. SIAM J. Numer. Anal. 43(3), 1321–1347 (2005)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007)

Marek, J.S.: Convergence of a generalized Newton and inexact generalized Newton algorithms for solving nonlinear equations with non differentiable terms. Numer. Algorithms 50(4), 401–415 (2008)

Haijun, W.: On new third-order convergent iterative formulas. Numer. Algorithms 48, 317–325 (2008)

Hueso, J.L., Martínez, E., Torregrosa, J.R.: Modified Newton’s method for systems of nonlinear equations with singular jacobian. J. Comput. Appl. Math. 224, 77–83 (2009)

Moreno, J.: Explicit construction of inverse function of polynomials. Int. J. Appl. Sci. Comput. 11(1), 53–64 (2004)

Moreno, J.: Inverse functions of polynomials around all its roots. Int. J. Appl. Sci. Comput. 11(2), 72–84 (2004)

Demidovich, B.P., Maron, I.A.: Cálculo Numérico Fundamental. Paraninfo, Madrid (1985)

Moreno, J., Casabán, M.C., Rodríguez-Álvarez, M.J.: An algorithm to initialize the search of solutions of polynomial systems. Comput. Math. Appl. 50, 919–933 (2005)

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem