Decomposability in fixed point computation with applications and acceleration techniques

An Analog Scheme for Fixed-Point Computation–Part II: Applications

In a companion paper [6] we presented theoretical analysis of an analog network for fixed-point computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear programming; 3) dynamic programing; and 4) network flow computations. Schematic circuits are proposed for r...

Secure Computation with Fixed-Point Numbers

Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that s...

Coupled fixed point results for $alpha$-admissible Mizoguchi-Takahashi contractions in $b$-metric spaces with applications

The aim of this paper is to  establish some fixed point theorems for $alpha$-admissible Mizoguchi-Takahashi contractive mappings defined on a ${b}$-metric space which generalize the results of Gordji and Ramezani cite{Roshan6}. As a result, we obtain some coupled fixed point theorems which generalize the results of '{C}iri'{c} {et al.} cite{Ciric3}. We also present  an application in order to i...

Anderson Acceleration for Fixed-Point Iterations

This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [Iterative procedures for nonlinear integral equations, J. Assoc. Comput. Machinery, 12 (1965), 547-560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anders...

Fixed Point Theorems and Applications