Algorithm 768: TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least-squares problems using tensor methods This article describes a modular software package for solving systems of nonlinear equations and nonlinear problems, using a new class of methods called tensor methods. It is intended for small- to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or to approximate it by finite differences at each iteration. The software allows the user to choose between a tensor method and a standard method based on a linear model. The tensor method approximates F(x) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies: a line search approach and a two-dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small- and medium-sized problems in iterations and function evaluations

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  1. Xie, Ze-Jia; Jin, Xiao-Qing; Wei, Yi-Min: Tensor methods for solving symmetric $\mathcal M$-tensor systems (2018)
  2. Boonyasiriwat, C.; Sikorski, K.; Tsay, C.: Circumscribed ellipsoid algorithm for fixed-point problems (2011)
  3. Sielemann, M.; Schmitz, G.: A quantitative metric for robustness of nonlinear algebraic equation solvers (2011)
  4. Rasch, Arno; Bücker, H. Martin: EFCOSS: an interactive environment facilitating optimal experimental design (2010)
  5. Bader, Brett W.; Schnabel, Robert B.: On the performance of tensor methods for solving ill-conditioned problems (2007)
  6. Honkala, M.; Roos, Janne; Karanko, V.: On nonlinear iteration methods for DC analysis of industrial circuits (2006)
  7. Bader, Brett W.: Tensor-Krylov methods for solving large-scale systems of nonlinear equations (2005)
  8. Motolese, Maurizio: Endogenous uncertainty and the non-neutrality of money (2004)
  9. Bader, Brett W.; Schnabel, Robert B.: Curvilinear linesearch for tensor methods (2003)
  10. Paprzycki, Marcin; Dent, Deborah; Kucaba-Piȩtal, Anna: Solvers for nonlinear algebraic equations; where are we today? (2002)
  11. Dent, Deborah; Paprzycki, Marcin; Kucaba-Piȩtal, Anna; Laudański, Ludomir: Studying the performance nonlinear systems solvers applied to the random vibration test (2001)
  12. Dent, Deborah; Paprzycki, M.; Kucaba-Pietal, Anna: Solvers for systems of nonlinear algebraic equations -- their sensitivity to starting vectors (2001)
  13. Motolese, Maurizio: Money non-neutrality in a rational belief equilibrium with financial assets (2001)
  14. Bouaricha, Ali; Schnabel, Robert B.: Tensor methods for large, sparse nonlinear least squares problems (2000)
  15. Dent, Deborah; Paprzycki, Marcin; Kucaba-Piȩral, Anna: Recent advances in solvers for nonlinear algebraic equations (2000)
  16. Gasparo, Maria Grazia: A nonmonotone hybrid method for nonlinear systems (2000)
  17. Holstad, Astrid: Numerical solution of nonlinear equations in chemical speciation calculations (1999)
  18. Bouaricha, Ali; Schnabel, Robert B.: Tensor methods for large sparse systems of nonlinear equations (1998)
  19. Bouaricha, Ali: Algorithm 765: STENMIN: A software package for large, sparse unconstrained optimization using tensor methods (1997)
  20. Bouaricha, Ali: Tensor methods for large, sparse unconstrained optimization (1997)

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