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This paper proposes a projection-based implicit modeling method (PIMM) for functionally graded lattice optimization, which does not require any homogenization techniques. In this method, a parametric projection function is proposed to link…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…
In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
We consider the problem of approximating all real roots of a square-free polynomial $f$. Given isolating intervals, our algorithm refines each of them to a width of $2^{-L}$ or less, that is, each of the roots is approximated to $L$ bits…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
Image matting is an important computer vision problem. Many existing matting methods require a hand-made trimap to provide auxiliary information, which is very expensive and limits the real world usage. Recently, some trimap-free methods…
This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Model-Based Iterative Reconstruction (MBIR) is important because direct methods, such as Filtered Back-Projection (FBP) can introduce significant noise and artifacts in sparse-angle tomography, especially for time-evolving samples. Although…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 $\AA$ and 10798 $\AA$ lines, which are sensitive to the coronal magnetic field. However, inverting such polarimetric…
Volume rendering using neural fields has shown great promise in capturing and synthesizing novel views of 3D scenes. However, this type of approach requires querying the volume network at multiple points along each viewing ray in order to…
Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such functions. Our approach extends approximation techniques for…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
Detection of objects is extremely important in various aerial vision-based applications. Over the last few years, the methods based on convolution neural networks have made substantial progress. However, because of the large variety of…