We consider the solution of sparse linear systems using direct methods via LU factorization. Unless the matrix is positive definite, numerical pivoting is usually needed to ensure stability, which is costly to implement especially in the sparse case. The Random Butterfly Transformations (RBT) technique provides an alternative to pivoting and is easily parallelizable. The RBT transforms the orig...

1 Background: The restoration of knee rotational stability after anatomical double 2 bundle anterior cruciate ligament (ACL) reconstruction has been demonstrated in 3 cadaveric model and passive stress test on human, but not yet in dynamic functional 4 biomechanical test performed by human subjects. 5 Purpose: The purpose of the current study was to prospectively investigate the range 6 of tibi...

Optimal sensor and actuator selection is a central challenge in high-dimensional estimation control. Nearly all subsequent control decisions are affected by these locations. In this article, we exploit balanced model reduction greedy optimization to efficiently determine selections that optimize observability controllability. particular, locations scalar measures of controllability using matrix...