Optimal algorithms for well-conditioned nonlinear systems of equations

IEEE Transactions on Computers

Volumn 50, Issue 7, 2001, Pages 689-698

  Bianchini, Monica ^b   Fanelli, Stefano ^c   Gori, Marco ^a,b  

^a IEEE   (Italy)

^b UNIVERSITY OF SIENA   (Italy)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Computational complexity; Nonlinear systems of equations; Parallel processing; Terminal attraction dynamics

Indexed keywords

OPTIMAL ALGORITHMS;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; GRADIENT METHODS; NONLINEAR EQUATIONS; OPTIMIZATION; PARALLEL PROCESSING SYSTEMS;

PROBLEM SOLVING;

EID: 0035390065     PISSN: 00189340     EISSN: None     Source Type: Journal    
DOI: 10.1109/12.936235     Document Type: Article

References (36)

1. Numerical solution of nonlinear-equations
2. A bisection method for systems of nonlinear equations
3. Computational implementation of the Multivariate Halley method for solving nonlinear systems of equations
4. ALGORITHM 652: HOMPACK: A suite of codes for globally convergent homotopy algorithms
5. The solutions of nonlinear systems of equations by second order systems of ordinary differential equations and linearly implicit a-stable techniques
6. Solving large nonlinear systems of equations by an adaptive condensation process
7. A class of direct methods for linear systems
8. The local convergence of ABS methods for nonlinear algebraic equations
9. Some efficient algorithms for solving systems of nonlinear equations
10. A quadratically convergent Newton-like method based upon Gaussian-elimination
11. On nonlinear generalized conjugate Gradient methods
12. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
13. Accelerated inexact Newton schemes for large systems of nonlinear equations
14. An overlaying technique for solving linear equations in real-time computing
15. QMR: A Quasi-minimal residual method for non-hermitian linear systems
16. A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems
17. Terminal attractors for addressable memory in neural networks
18. Terminal attractors in neural networks
19. Terminal attractor learning algorithms for backpropagation neural networks
20. Testing unconstrained optimization software
21. Iterative algorithms for solution of large sparse eystems of linear equations on hypercubes
22. The computation and communication complexity of a parallel banded system solver
23. Parallel minimal norm method for tridiagonal linear systems
24. Algorithm-based error-detection schemes for iterative solution of partial differential equations
25. An estimate for the condition number of a matrix
26. Estimating matrix condition numbers
27. A set of counter-examples to three condition number estimators
28. Condition estimates