A penalty continuation method for the ∓∞ solution of overdetermined linear systems

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Solution to Overdetermined Linear Equations

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m n) matrix A and the data vector b. This is in contrast to a least squares solution, whe...

Least squares solution of nearly square overdetermined sparse linear systems

The solution of nearly square overdetermined linear systems is studied. The sparse QR technique is compared with two sparse LU-based techniques. Numerical tests with realworld and artificial matrices indicate that the LU techniques are more accurate for incompatible right-hand sides. Also, the amount of floating point operations required by LU techniques is approximately one half smaller than Q...

A New Algorithm for the Chebyshev Solution of Overdetermined Linear Systems

Let x(p) be the point which minimizes the residual of a linear system in the lv norm. It is known that under certain conditions x(p) —» x*, the Chebyshev or /„ solution, as p —y <*>. A differential equation describing x(p) is derived from which an iterative scheme is devised. A convergence analysis is given and numerical results are presented.

Solution of Fully Fuzzy Linear Systems by ST Method