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When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
Individualized manufacturing is becoming an important approach as a means to fulfill increasingly diverse and specific consumer requirements and expectations. While there are various solutions to the implementation of the manufacturing…
One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered…
Efficient deep learning computing requires algorithm and hardware co-design to enable specialization: we usually need to change the algorithm to reduce memory footprint and improve energy efficiency. However, the extra degree of freedom…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
Recently, the demand of low-power deep-learning hardware for industrial applications has been increasing. Most existing artificial intelligence (AI) chips have evolved to rely on new chip technologies rather than on radically new hardware…
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…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
Approximate computing methods have shown great potential for deep learning. Due to the reduced hardware costs, these methods are especially suitable for inference tasks on battery-operated devices that are constrained by their power budget.…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Similar to algorithms, which consume time and memory to run, hardware requires resources to function. For devices processing physical waves, implementing operations needs sufficient "space," as dictated by wave physics. How much space is…
Space-filling designs are commonly used in computer experiments to fill the space of inputs so that the input-output relationship can be accurately estimated. However, in certain applications such as inverse design or feature-based…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
In the last few years, the notion of optimal polynomial approximant has appeared in the mathematics literature in connection with Hilbert spaces of analytic functions of one or more variables. In the 70s, researchers in engineering and…