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Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically…
This thesis explores parameter estimation methods for rapidly reconstructing compact binary sources generating gravitational waves. It employs numerical linear algebra and meshfree approximation techniques to expedite waveform generation…
We investigate Nordstr\"om's second theory of gravitation, with a focus on utilizing it as a testbed for developing techniques in numerical relativity. Numerical simulations of inspiraling compact star binaries are performed for this…
Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
In this work we have used for the first time pseudo-spectral methods to perform numerical simulations of spherically symmetric black hole formations on a Friedman-Robertson-Walker universe. With these methods, the differential equations…
Input binarization has shown to be an effective way for network acceleration. However, previous binarization scheme could be regarded as simple pixel-wise thresholding operations (i.e., order-one approximation) and suffers a big accuracy…
The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. However, the merit factor problem is…
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…
We propose a technique for accurate, flexible and robust generation of arbitrary coherent superpositions of two quantum states. It uses a sequence of two adiabatic pulses split by a phase jump serving as a control parameter. Each pulse has…
The orbital and eccentricity evolution for compact object binaries through gravitational wave emission first derived by Peters and Mathews are used extensively throughout the gravitational wave community for calculating the orbital…
It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using black hole perturbation theory applied to various invariants. For instance, a computation of the…
Numerical relativity simulations provide a full description of the dynamics of binary systems, including gravitational radiation. The waveforms produced by these simulations have a number of applications in gravitational-wave detection and…
We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation to assume that (1) the binary star system is irrotational, i.e. the…
We present a simple yet powerful technique for forming iterative methods of various convergence orders. Methods of various convergence orders (four, six, eight and ten) are formed through a modest modification of the classical Newton…
Experimental results show that, when the order $n$ is odd, there are de Bruijn sequences such that the corresponding complement sequence and the reverse sequence are the same. In this paper, we propose one efficient method to generate such…
We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the run-time we are able to retrieve the most…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…