Related papers: On iterated interpolation
Kernel interpolation, especially in the context of Gaussian process emulation, is a widely used technique in surrogate modelling, where the goal is to cheaply approximate an input-output map using a limited number of function evaluations.…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…
Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the "interpolation kernel", an analytic continuation of the author's elliptic…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…