Related papers: Multi-dimensional interpolations in C++
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…
Computational notebooks, widely used for ad-hoc analysis and often shared with others, can be difficult to understand because the standard linear layout is not optimized for reading. In particular, related text, code, and outputs may be…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
Designing multiscale visualizations, particularly when the ratio between the largest scale and the smallest item is large, can be challenging, and designers have developed many approaches to overcome this challenge. We present a design…
We describe the application of a scalable algorithm for interpolating solution data in the overlapping mesh region of two solvers. This feature is essential to obtain a globally consistent solution for in-situ coupled atmospheric wave…
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…
The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever…
Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it…
We present POLO --- a C++ library for large-scale parallel optimization research that emphasizes ease-of-use, flexibility and efficiency in algorithm design. It uses multiple inheritance and template programming to decompose algorithms into…
Expression templates are a well-known set of techniques for improving the efficiency of operator overloading-based forward mode automatic differentiation schemes in the C++ programming language by translating the differentiation from…
We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…
We introduce process-oriented programming as a natural extension of object-oriented programming for parallel computing. It is based on the observation that every class of an object-oriented language can be instantiated as a process,…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
For high dimensional problems, such as approximation and integration, one cannot afford to sample on a grid because of the curse of dimensionality. An attractive alternative is to sample on a low discrepancy set, such as an integration…
The development of the mlpack C++ machine learning library (http://www.mlpack.org/) has required the design and implementation of a flexible, robust optimization system that is able to solve the types of arbitrary optimization problems that…
Interoperability is the ability of a programming language to work with systems based on different languages and paradigms. These days, many widely used high-level language impementations provide access to external functionalities. In this…
In type theory, we can express many practical ideas by attributing some additional data to expressions we operate on during compilation. For instance, some substructural type theories augment variables' typing judgments with the information…
In this work, we first propose a fully differentiable Many-to-Many (M2M) splatting framework to interpolate frames efficiently. Given a frame pair, we estimate multiple bidirectional flows to directly forward warp the pixels to the desired…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…