Related papers: A Simple Derivation of Newton-Cotes Formulas with …
We study the doubly nonnegative (DNN) relaxation of the standard quadratic optimization problem \[ \min\{x^\top Qx:\ x\in\Delta^{n-1}\},\qquad \Delta^{n-1}:=\{x\in\mathbb{R}_+^n:\ \mathbb{1}^\top x=1\}, \] for random symmetric matrices with…
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible…
A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…
We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures is computation of a quotient for long division. We give…
The MultiExp Gaussian quadrature rule proposed by Gill and Chien has many compelling properties for the integration of radial integrands encountered in electronic structure, but thus far has only been computed up to N = 50, with some…
In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
We discuss the close connection between eigenvalue computation and optimization using the Newton method and subspace methods. From the connection we derive a new class of Newton updates. The new update formulation is similar to the…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient…
Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution…
Leibniz's rule for the $n$-th derivative of a product is a very well known and extremely useful formula. In this article, we introduce an analogous explicit formula for the $n$-th derivative of a quotient of two functions. Later, we use…
The trigonometric interpolants to a periodic function $f$ in equispaced points converge if $f$ is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if $f$ is continuous. What if the points are…
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Bj\"{o}rck and Pereyra algorithm for solving…
In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial operator. Both the initial value problem and the…
The problem of minimizing an objective that can be written as the sum of a set of $n$ smooth and strongly convex functions is considered. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and…
For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters.…
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…
The method of regularized stokeslets is a powerful numerical method to solve the Stokes flow equations for problems in biological fluid mechanics. A recent variation of this method incorporates a nearest-neighbor discretization to improve…