**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Splines: Least-Squares Method

Description

This lecture covers the continuation of splines, focusing on the least-squares method for interpolating splines and the not-a-knot interpolating spline. The instructor explains the constraints needed for the natural cubic interpolating spline and demonstrates the process using MATLAB. The lecture concludes with the computation of the least-squares approximant for polynomial functions of various degrees.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (177)

Soviet Union

The Soviet Union, officially the Union of Soviet Socialist Republics (USSR), was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR.

European Union

The European Union (EU) is a supranational political and economic union of member states that are located primarily in Europe. The union has a total area of and an estimated total population of over 448 million. The EU has often been described as a sui generis political entity (without precedent or comparison) combining the characteristics of both a federation and a confederation. Containing 5.

Spline interpolation

In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-ten polynomial to all of them.

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.

Hermite polynomials

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term is present); systems theory in connection with nonlinear operations on Gaussian noise.

Related lectures (673)

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Error Analysis and InterpolationMATH-251(a): Numerical analysis

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Piecewise Polynomial Interpolation: Splines

Covers piecewise polynomial interpolation with splines, focusing on Lagrange interpolation with Chebyshev nodes and error convergence.

Interpolation and Curve Fitting

Explores interpolation and curve fitting techniques using MATLAB for analyzing experimental data and smoothing curves.

Linear RegressionPHYS-467: Machine learning for physicists

Covers the concept of linear regression, including polynomial regression and hyperparameters selection.