Direct iterative methods for least-squares solutions to singular operator equations

Iterative least-squares solutions of coupled Sylvester matrix equations

In this paper, we present a general family of iterative methods to solve linear equations, which includes the well-known Jacobi and Gauss–Seidel iterations as its special cases. The methods are extended to solve coupled Sylvester matrix equations. In our approach, we regard the unknown matrices to be solved as the system parameters to be identified, and propose a least-squares iterative algorit...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Least squares solutions of bilinear equations

In this second recitation, we will address the following topics: • Review of the projection theorem. • Derivation of the projection operator on the range of a matrix, using completion of squares. • Solutions of under and over constrained linear equations. Notice that this recitation note is an alternative discussion of the least-squares problem which is more difficult than the one you can find ...

least squares solutions of inconsistent fuzzy linear matrix equations

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Preconditioned Iterative Methods for Solving Linear Least Squares Problems

New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...