In Computational Structure Mechanics (CSM) the continuum media under study is modeled by a bunch of nodes. The well known technique of Finite Element Method (FEM) is a CSM routine devised to correlate the force and deflection of the nodes. In a direct FEM problem, in each node just one of the force or their associated displacement components is unspecified. Then if in some nodes both force and displacement components are unknowns, the problem is called an inverse problem. A typical inverse problem for a beam is the estimation of load on the beam by measuring its displacement. The solutions of inverse problems are naturally sensitive to the input data and are classified as ill-posed problems. In practice the FEM modeling of a CSM inverse problem results in a sparse, un-symmetric, and often rectangular stiffness matrix. A through treatment of the problem is given in [1]. There are both iterative and non-iterative methods of solution for such a problem. One of the well-known iterative techniques is the method of Least Squares (LSQR). As it can be seen in [2], the function of the method may be improved by invoking of some additional matrix manipulations known as preconditioning and column scaling. Here in this work to improve the results of the application of LSQR method in CSM problems the use of some pre-conditioners and column scaling techniques are introduced. To this ends, the estimations of the end load of a cantilever beam is selected as the case study. The numerical results show that LSQR method with the pre-conditioners known as AINV and CIMGS are the proper combinations for the solution technique. It is also shown that a definite norm known as \\\"condition number\\\" is a good criterion for the evaluation of the solution accuracy.

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