Solutions of Linear Equations

Solutions of Linear Equations

For simplicity, we follow the rules: x denotes a set, i, j, k, l, m, n denote natural numbers, K denotes a field, N denotes a without zero finite subset of N, a, b denote elements of K, A, B, B1, B2, X, X1, X2 denote matrices over K, A′ denotes a matrix over K of dimension m × n, B′ denotes a matrix over K of dimension m × k, and M denotes a square matrix over K of dimension n. We now state a n...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Continuous Solutions of Linear Equations

Enclosing Solutions of Linear Equations

It is shown that Rump’s method for enclosing solutions of linear equations can be reformulated in an interval–free form and that the underlying inclusion result can be proved by elementary means without using Brouwer’s fixed–point theorem. A sufficient condition on Rump’s “inflation parameter” ε is given under which finite termination occurs. Also, a more general modified algorithm is studied f...