High accuracy computation with linear analog optical systems: a critical study

High accuracy optical processors based on the algorithm of digital multiplication by analog convolution (DMAC) are studied for ultimate performance limitations. Variations of optical processors that perform high accuracy vector-vector inner products are studied in abstract and with specific examples. It is concluded that the use of linear analog optical processors in performing digital computations with DMAC leads to impractical requirements for the accuracy of analog optical systems and the complexity of postprocessing electronics

Limited-memory BFGS Systems with Diagonal Updates

In this paper, we investigate a formula to solve systems of the form (B + {\sigma}I)x = y, where B is a limited-memory BFGS quasi-Newton matrix and {\sigma} is a positive constant. These types of systems arise naturally in large-scale optimization such as trust-region methods as well as doubly-augmented Lagrangian methods. We show that provided a simple condition holds on B_0 and \sigma, the system (B + \sigma I)x = y can be solved via a recursion formula that requies only vector inner products. This formula has complexity M^2n, where M is the number of L-BFGS updates and n >> M is the dimension of x