Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Error Analysis and Interpolation

In course

MATH-251(a): Numerical analysis

This course presents numerical methods to solve mathematical problems such as systems of linear and nonlinear equations, function approximation, integration and differentiation, and differential equations. ...

Description

This lecture covers error analysis in interpolation, discussing limitations and stability when interpolating data on evenly distributed nodes. It explores the polynomial of degree, Lagrange base, and reliability. The instructor demonstrates applications using Jupyter Notebooks for polynomial interpolation.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (4)

Daniel Kressner

Pablo Antolin Sanchez

Fabio Nobile

Espen Sande

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.

Interpolation

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 engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Trigonometric interpolation

In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions. An important special case is when the given data points are equally spaced, in which case the solution is given by the discrete Fourier transform.

Lagrange polynomial

In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs with the are called nodes and the are called values. The Lagrange polynomial has degree and assumes each value at the corresponding node, Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler.

Multivariate interpolation

In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).

Related lectures (38)

Interpolation de fonction

Explores interpolation of regular functions, error analysis, convergence, and Chebyshev polynomials.

Reed Solomon Codes: Basics and Applications

Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Interpolation by Intervals: Lagrange Interpolation

Covers Lagrange interpolation using intervals to find accurate polynomial approximations.

Polynomial Interpolation: Optimizing Error