Related papers: Application of accelerated fixed-point algorithms …
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
Robotic affordance estimation is challenging due to visual, geometric, and semantic ambiguities in sensory input. We propose a method that disambiguates these signals using two coupled recursive estimators for sub-aspects of affordances:…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…
A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…
We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network,…
Analysis of pipe networks involves computing flow rates and pressure differences on pipe segments in the network, given the external inflow/outflow values. This analysis can be conducted using iterative methods, among which the algorithms…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles and approximate triples…
Smoothing is essential to many oceanographic, meteorological and hydrological applications. The interval smoothing problem updates all desired states within a time interval using all available observations. The fixed-lag smoothing problem…
The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for…
Non-trivial analysis problems require posets with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint…
Finding a fixed point to a nonexpansive operator, i.e., $x^*=Tx^*$, abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic…
Anderson acceleration (AA) has a long history of use and a strong recent interest due to its potential ability to dramatically improve the linear convergence of the fixed-point iteration. Most authors are simply using and analyzing the…
Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…
The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…