This paper presents an example of an algebraic eigenvalue problem which can be used to motivate the study of numerical techniques for solving such problems. The problem consists of finding the axis and angle of rotation from a 3 x 3 rotation matrix and is referred to as the axis-angle problem. The problem is used to demonstrate the inverse power method for finding eigenvectors. The axis-angle p...

Power Method We now describe the power method for computing the dominant eigenpair. Its extension to the inverse power method is practical for finding any eigenvalue provided that a good initial approximation is known. Some schemes for finding eigenvalues use other methods that converge fast, but have limited precision. The inverse power method is then invoked to refine the numerical values and...

Assessment of the correlation between rock brittleness and rock fracture toughness has been the subject of extensive research works in the recent years. Unfortunately, the brittleness measurement methods have not yet been standardized, and rock fracture toughness cannot be estimated satisfactorily by the proposed indices. In the present study, statistical analyses are performed on some data col...

We propose a new automatic program inversion method for imperative programs that contain loops. In particular, given a loop that produces an output state given a particular input state, our method can synthesize an inverse loop that reconstructs the input state given the original loop’s output state. The synthesis process consists of two major components: (a) building the inverse loop’s body, a...

this paper proposes a new approach for determining efficient dmus in dea models using inverse optimi-zation and without solving any lps. it is shown that how a two-phase algorithm can be applied to detect effi-cient dmus. it is important to compare computational performance of solving the simultaneous linear equa-tions with that of the lp, when computational issues and complexity analysis are a...

The calculation of forces in the kinematic pairs of mechanisms by inverse dynamics is usually performed without friction considerations. In practice, when examination of articulated mechanisms takes into account friction, the solution of the inverse dynamics results in a complex procedure. If a modular approach for the inverse dynamics is used, then exact solutions are available, but not necess...

We explore robust methods of automatically quantifying constriction location, constriction degree and gestural kinematics of Italian short and long consonants using direct image analysis techniques applied to rtMRI data. Articulatory kinematics are estimated from correlated regional changes in pixel intensity. We demonstrate that these methods are capable of quantifying differences in constrict...

The mechanical conditions in the repair tissues are known to influence the outcome of fracture healing. These mechanical conditions are determined by the stiffness of fixation and limb loading. Experimental studies have shown that there is a range of beneficial fixation stiffness for timely healing and that fixation stiffness that is either too flexible or too stiff impairs callus healing. Howe...