Relative Errors Versus Residuals of Approximate Solutions to Linear Algebraic Equations and Least Squares Problems

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

least squares solutions of inconsistent fuzzy linear matrix equations

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least squares solutions of inconsistent fuzzy linear matrix equations

Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

Least-squares collocation for linear higher-index differential-algebraic equations

Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential-algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discreti...