• Publications
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Iterative methods for sparse linear systems
  • Y. Saad
  • Computer Science, Mathematics
  • 1 May 2003
TLDR
Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I . Expand
A Flexible Inner-Outer Preconditioned GMRES Algorithm
  • Y. Saad
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 1 March 1993
TLDR
A variant of the GMRES algorithm is presented that allows changes in the preconditioning at every step. Expand
Analysis of some Krylov subspace approximations to the matrix exponential operator
In this note a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation $\exp (A)v$ is presented, and a priori and a posteriors error estimates are established.Expand
Hybrid Krylov Methods for Nonlinear Systems of Equations
  • P. Brown, Y. Saad
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 1 May 1990
TLDR
In this paper, several implementations of Newton-like iteration schemes based on Krylov subspace projection methods for solving nonlinear equations are considered. Expand
ILUT: A dual threshold incomplete LU factorization
  • Y. Saad
  • Mathematics, Computer Science
  • Numer. Linear Algebra Appl.
  • 1 July 1994
TLDR
In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. Expand
Topological properties of hypercubes
TLDR
The n-dimensional hypercube is a highly concurrent loosely coupled multiprocessor based on the binary n-cube topology. Expand
Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique
  • E. Kokiopoulou, Y. Saad
  • Mathematics, Computer Science
  • IEEE Transactions on Pattern Analysis and Machine…
  • 1 December 2007
TLDR
We propose a method, named orthogonal neighborhood preserving projections, which works by first building an "affinity" graph for the data in a way that is similar to the method of locally linear embedding (LLE). Expand
Krylov subspace methods for solving large unsymmetric linear systems
Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r/sub 0/, Ar/sub 0/,..., A/sup m-1/r/sub 0/) are developed, generalizing the method of conjugate gradients toExpand
Experimental study of ILU preconditioners for indefinite matrices
Incomplete LU factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices. However, their failure rate is still too high for them toExpand
Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
Abstract It is shown that the method of Arnoldi can be successfully used for solvinglarge unsymmetric eigenproblems. Like the symmetric Lanczos method, Arnoldi's algorithm realizes a projectionExpand
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