51,232 research outputs found
Impact of Accuracy Optimization on the Convergence of Numerical Iterative Methods
Among other objectives, rewriting programs serves as a useful
technique to improve numerical accuracy. However, this optimization
is not intuitive and this is why we switch to automatic transformation
techniques. We are interested in the optimization of numerical programs
relying on the IEEE754 oating-point arithmetic. In this article, our
main contribution is to study the impact of optimizing the numerical accuracy
of programs on the time required by numerical iterative methods
to converge. To emphasize the usefulness of our tool, we make it optimize
several examples of numerical methods such as Jacobi's method,
Newton-Raphson's method, etc. We show that significant speedups are
obtained in terms of number of iterations, time and
ops
Regularized Nonlinear Acceleration
We describe a convergence acceleration technique for unconstrained
optimization problems. Our scheme computes estimates of the optimum from a
nonlinear average of the iterates produced by any optimization method. The
weights in this average are computed via a simple linear system, whose solution
can be updated online. This acceleration scheme runs in parallel to the base
algorithm, providing improved estimates of the solution on the fly, while the
original optimization method is running. Numerical experiments are detailed on
classical classification problems
Dissipative Quantum Dynamics and Optimal Control using Iterative Time Ordering: An Application to Superconducting Qubits
We combine a quantum dynamical propagator that explicitly accounts for
quantum mechanical time ordering with optimal control theory. After analyzing
its performance with a simple model, we apply it to a superconducting circuit
under so-called Pythagorean control. Breakdown of the rotating-wave
approximation is the main source of the very strong time-dependence in this
example. While the propagator that accounts for the time ordering in an
iterative fashion proves its numerical efficiency for the dynamics of the
superconducting circuit, its performance when combined with optimal control
turns out to be rather sensitive to the strength of the time-dependence. We
discuss the kind of quantum gate operations that the superconducting circuit
can implement including their performance bounds in terms of fidelity and
speed.Comment: 16 pages, 11 figure
Hardware Impairments Aware Transceiver Design for Full-Duplex Amplify-and-Forward MIMO Relaying
In this work we study the behavior of a full-duplex (FD) and
amplify-and-forward (AF) relay with multiple antennas, where hardware
impairments of the FD relay transceiver is taken into account. Due to the
inter-dependency of the transmit relay power on each antenna and the residual
self-interference in an FD-AF relay, we observe a distortion loop that degrades
the system performance when the relay dynamic range is not high. In this
regard, we analyze the relay function in presence of the hardware inaccuracies
and an optimization problem is formulated to maximize the signal to
distortion-plus-noise ratio (SDNR), under relay and source transmit power
constraints. Due to the problem complexity, we propose a
gradient-projection-based (GP) algorithm to obtain an optimal solution.
Moreover, a nonalternating sub-optimal solution is proposed by assuming a
rank-1 relay amplification matrix, and separating the design of the relay
process into multiple stages (MuStR1). The proposed MuStR1 method is then
enhanced by introducing an alternating update over the optimization variables,
denoted as AltMuStR1 algorithm. It is observed that compared to GP, (Alt)MuStR1
algorithms significantly reduce the required computational complexity at the
expense of a slight performance degradation. Finally, the proposed methods are
evaluated under various system conditions, and compared with the methods
available in the current literature. In particular, it is observed that as the
hardware impairments increase, or for a system with a high transmit power, the
impact of applying a distortion-aware design is significant.Comment: Submitted to IEEE Transactions on Wireless Communication
Improving Performance of Iterative Methods by Lossy Checkponting
Iterative methods are commonly used approaches to solve large, sparse linear
systems, which are fundamental operations for many modern scientific
simulations. When the large-scale iterative methods are running with a large
number of ranks in parallel, they have to checkpoint the dynamic variables
periodically in case of unavoidable fail-stop errors, requiring fast I/O
systems and large storage space. To this end, significantly reducing the
checkpointing overhead is critical to improving the overall performance of
iterative methods. Our contribution is fourfold. (1) We propose a novel lossy
checkpointing scheme that can significantly improve the checkpointing
performance of iterative methods by leveraging lossy compressors. (2) We
formulate a lossy checkpointing performance model and derive theoretically an
upper bound for the extra number of iterations caused by the distortion of data
in lossy checkpoints, in order to guarantee the performance improvement under
the lossy checkpointing scheme. (3) We analyze the impact of lossy
checkpointing (i.e., extra number of iterations caused by lossy checkpointing
files) for multiple types of iterative methods. (4)We evaluate the lossy
checkpointing scheme with optimal checkpointing intervals on a high-performance
computing environment with 2,048 cores, using a well-known scientific
computation package PETSc and a state-of-the-art checkpoint/restart toolkit.
Experiments show that our optimized lossy checkpointing scheme can
significantly reduce the fault tolerance overhead for iterative methods by
23%~70% compared with traditional checkpointing and 20%~58% compared with
lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
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