In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points.
In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular, such as predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute.
In mathematics, a time series is a series of data points indexed in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.
In mathematics and numerical analysis, the Ricker wavelet
In mathematics a radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, either the origin, so that , or some other fixed point , called a center, so that . Any function that satisfies the property is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection which forms a basis for some function space of interest, hence the name.
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field.
Richard Steven Varga was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including matrix analysis, complex analysis, approximation theory, and scientific computation. He was the author of the classic textbook Matrix Iterative Analysis. Varga served as the Editor-in-Chief of the journal Electronic Transactions on Numerical Analysis (ETNA).
Peter Wynn (1931—2017) was an English mathematician. His main achievements concern approximation theory – in particular the theory of Padé approximants – and its application in numerical methods for improving the rate of convergence of sequences of real numbers.
Hans Georg Feichtinger is an Austrian mathematician. He is Professor in the mathematical faculty of the University of Vienna. He is editor-in-chief of the Journal of Fourier Analysis and Applications (JFAA) and associate editor to several other journals. He is one of the founders and head of the Numerical Harmonic Analysis Group (NuHAG) at University of Vienna. Today Feichtinger's main field of research is harmonic analysis with a focus on time-frequency analysis.
In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines) and are generally used for multivariate approximation/interpolation. Geometrically, a box spline is the shadow (X-ray) of a hypercube projected down to a lower-dimensional space. Box splines and simplex splines are well studied special cases of polyhedral splines which are defined as shadows of general polytopes.
Lee Albert Rubel was a mathematician known for his contributions to analog computing.
In the mathematical field of numerical analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline. A discrete spline is a piecewise polynomial such that its central differences are continuous at the knots whereas a spline is a piecewise polynomial such that its derivatives are continuous at the knots. Discrete cubic splines are discrete splines where the central differences of orders 0, 1, and 2 are required to be continuous.
Theodore Joseph Rivlin was an American mathematician, specializing in approximation theory. He is known for his 1969 book An Introduction to the Approximation of Functions, which became a standard text.
Edward Barry Saff is an American mathematician, specializing in complex analysis, approximation theory, numerical analysis, and potential theory.
Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations.
Christian Reinsch was a German mathematician who worked in the area of numerical analysis.
Charles William Clenshaw was an English mathematician, specializing in numerical analysis. He is known for the Clenshaw algorithm (1955) and Clenshaw–Curtis quadrature (1960). In a 1984 paper Beyond Floating Point, Clenshaw and Frank W. J. Olver introduced symmetric level-index arithmetic.
Albert Cohen is a French mathematician, specializing in approximation theory, numerical analysis, and digital signal processing.
Probabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
