Journal ArticleDOI
A class of direct methods for linear systems
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In this article, a class of methods of direct type for solving determined or underdetermined, full rank or deficient rank linear systems is presented and theoretically analyzed, which can be considered as a generalization of the methods of Brent and Brown as restricted to linear systems and implicitly contains orthogonal, LU and LL T factorization methods.Abstract:
A class of methods of direct type for solving determined or underdetermined, full rank or deficient rank linear systems is presented and theoretically analyzed. The class can be considered as a generalization of the methods of Brent and Brown as restricted to linear systems and implicitly contains orthogonal,LU andLL T factorization methods.read more
Citations
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Journal ArticleDOI
CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm
TL;DR: A new method similar to QMR but based on the Hessenberg process instead of the Lanczos process is given, which is less expensive and requires slightly less storage than GMRES.
Book ChapterDOI
Algorithms for Solving Nonlinear Systems of Equations
TL;DR: Numerical methods for solving nonlinear systems of equations F (x) = 0, where F: R n— R n is surveyed, especially interested in large problems.
Journal ArticleDOI
A direct projection method for sparse linear systems
Michele Benzi,Carl D. Meyer +1 more
TL;DR: When a sparsity-preserving pivoting strategy is incorporated, it is demonstrated that the oblique projection technique can be superior, in terms of both fill-in and arithmetic complexity, to more standard sparse algorithms based on gaussian elimination.
Posted Content
ABS Methods and ABSPACK for Linear Systems and Optimization, a Review
TL;DR: ABS methods are a large class of methods, based upon the Egervary rank reducing algebraic process, first introduced in 1984 by Abaffy, Broyden and Spedicato for solving linear algebraic systems, and later extended to nonlinear algebraic equations, to optimization problems and other fields; software based upon ABS methods are now under development.
Journal ArticleDOI
ABS methods and ABSPACK for linear systems and optimization: A review
TL;DR: This paper reviews ABS methods for linear systems and optimization, from both the point of view of theory and the numerical performance of ABSPACK.
References
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Journal ArticleDOI
The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints
TL;DR: The gradient projection method was originally presented to the American Mathematical Society for solving linear programming problems by Dantzig et al. as discussed by the authors, and has been applied to nonlinear programming problems as well.
Journal ArticleDOI
The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
TL;DR: In this paper, the authors present some methods in the general setting of oblique projection methods and give some theoretical results for large nonsymmetric systems, and some experiments comparing the various algorithms are reported.
Journal ArticleDOI
A Quadratically Convergent Newton-Like Method Based Upon Gaussian-Elimination
TL;DR: The method is a variation of Newton's method incorporating Gaussian elimination in such a way that the most recent information is always used at each step of the algorithm, and it is proved that the iteration converges locally and that the convergence is quadratic in nature.
Journal ArticleDOI
Conjugate direction methods for solving systems of linear equations
TL;DR: A generalization of the notion of a set of directions conjugate to a matrix is shown to lead to a variety of finitely terminating iterations for solving systems of linear equations.
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