3,935 research outputs found
Table-Free Seed Generation for Hardware Newton–Raphson Square Root and Inverse Square Root Implementations in IoT Devices
ConsejerÃaa de EconomÃa y Conocimiento de la Junta de AndalucÃa y el Fondo Europeo de Desarrollo Regional (FEDER) bajo el proyecto B-TIC-588-UGR2
A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations
A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation
Characterization and Implementation of a Real-World Target Tracking Algorithm on Field Programmable Gate Arrays with Kalman Filter Test Case
A one dimensional Kalman Filter algorithm provided in Matlab is used as the basis for a Very High Speed Integrated Circuit Hardware Description Language (VHDL) model. The JAVA programming language is used to create the VHDL code that describes the Kalman filter in hardware which allows for maximum flexibility. A one-dimensional behavioral model of the Kalman Filter is described, as well as a one-dimensional and synthesizable register transfer level (RTL) model with optimizations for speed, area, and power. These optimizations are achieved by a focus on parallelization as well as careful Kalman filter sub-module algorithm selection. Newton-Raphson reciprocal is the chosen algorithm for a fundamental aspect of the Kalman filter, which allows efficient high-speed computation of reciprocals within the overall system. The Newton-Raphson method is also expanded for use in calculating square-roots in an optimized and synthesizable two-dimensional VHDL implementation of the Kalman filter. The two-dimensional Kalman filter expands on the one-dimensional implementation allowing for the tracking of targets on a real-world Cartesian coordinate system
Nonlinear optimal guidance algorithms Interim report
Nonlinear optimal guidance algorithms for space mission
Testing Monotonicity of Pricing Kernels
The behaviour of market agents has always been extensively covered in the literature. Risk averse behaviour, described by von Neumann and Morgenstern (1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over uncertain choice with the same expected value, however lately there has been a lot of discussion about the reliability of this approach. Some authors have shown that there is a reference point where market utility functions are convex. In this paper we have constructed a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotone decreasing EPK corresponds to a concave utility function while non-monotone decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigated the EPK for German DAX data for years 2000, 2002 and 2004 and found the evidence of non-concave utility functions: H0 hypothesis of monotone decreasing pricing kernel was rejected at 5% and 10% significance level in 2002 and at 10% significance level in 2000.Risk Aversion, Pricing kernel
Multivariate GARCH estimation via a Bregman-proximal trust-region method
The estimation of multivariate GARCH time series models is a difficult task
mainly due to the significant overparameterization exhibited by the problem and
usually referred to as the "curse of dimensionality". For example, in the case
of the VEC family, the number of parameters involved in the model grows as a
polynomial of order four on the dimensionality of the problem. Moreover, these
parameters are subjected to convoluted nonlinear constraints necessary to
ensure, for instance, the existence of stationary solutions and the positive
semidefinite character of the conditional covariance matrices used in the model
design. So far, this problem has been addressed in the literature only in low
dimensional cases with strong parsimony constraints. In this paper we propose a
general formulation of the estimation problem in any dimension and develop a
Bregman-proximal trust-region method for its solution. The Bregman-proximal
approach allows us to handle the constraints in a very efficient and natural
way by staying in the primal space and the Trust-Region mechanism stabilizes
and speeds up the scheme. Preliminary computational experiments are presented
and confirm the very good performances of the proposed approach.Comment: 35 pages, 5 figure
Numerical Methods for the QCD Overlap Operator IV: Hybrid Monte Carlo
The extreme computational costs of calculating the sign of the Wilson matrix
within the overlap operator have so far prevented four dimensional dynamical
overlap simulations on realistic lattice sizes, because the computational power
required to invert the overlap operator, the time consuming part of the Hybrid
Monte Carlo algorithm, is too high. In this series of papers we introduced the
optimal approximation of the sign function and have been developing
preconditioning and relaxation techniques which reduce the time needed for the
inversion of the overlap operator by over a factor of four, bringing the
simulation of dynamical overlap fermions on medium-size lattices within the
range of Teraflop-computers.
In this paper we adapt the HMC algorithm to overlap fermions. We approximate
the matrix sign function using the Zolotarev rational approximation, treating
the smallest eigenvalues of the Wilson operator exactly within the fermionic
force. We then derive the fermionic force for the overlap operator, elaborating
on the problem of Dirac delta-function terms from zero crossings of eigenvalues
of the Wilson operator. The crossing scheme proposed shows energy violations
which are better than O() and thus are comparable with the
violations of the standard leapfrog algorithm over the course of a trajectory.
We explicitly prove that our algorithm satisfies reversibility and area
conservation. Finally, we test our algorithm on small , , and
lattices at large masses.Comment: v2 60 pages; substantial changes to all parts of the article; v3
minor revsion
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