Lagrange interpolation example. Example No 1: Interpolate the value of the function corresponding to $$X = 4$$ using Lagrange’s interpolation formula from the following set of data: The Newton’s forward and backward interpolation formulae can be used only when the values of x are at equidistant. Home > Numerical methods calculators > Numerical Interpolation using Lagrange's Interpolation formula example In the case of Lagrange interpolation, we have m different numbers x0; x1; : : : ; xm 2 R and take function evaluations up to order m, to construct a degree m polynomial p(x) with We choose 11 equally spaced points in the interval and form the Lagrange form of the interpolating polynomial using MATLAB. Jul 23, 2025 · In this article, we will learn about, Lagrange Interpolation, Lagrange Interpolation Formula, Proof for Lagrange Interpolation Formula, Examples based on Lagrange Interpolation Formula, and others in detail. In other words interpolation is the technique to estimate the value of a mathematical function, for any intermediate value of the independent variable. In the first-order case, it reduces to linear interpolation. Sep 23, 2022 · On this page, the definition and properties of Lagrange interpolation and examples (linear interpolation, quadratic interpolation, cubic interpolation) are described with solutions and proofs. . Learn how to find its first, second, third, and nth order with equations and examples. It is also called Waring-Lagrange interpolation, since Waring actually published it 16 years before Lagrange [312, p. Refer to the code below for a very naive O(n3) implementation. 323]. The entries in the table will have eight accurate decimal places and we will linearly interpolate between adjacent entries to determine intermediate values. Example Suppose we are preparing a table of values for cos x on [0, π]. What should the spacing between adjacent The Lagrange interpolation formula is a way to find a polynomial, called Lagrange polynomial, that takes on certain values at arbitrary points. Jul 23, 2025 · Interpolation is a method of finding new data points within the range of a discrete set of known data points (Source Wiki). Dec 11, 2024 · What is the Lagrange interpolation polynomial. More generically, the term polynomial interpolation normally refers to Lagrange interpolation. Learn about Lagrange interpolation, its types, applications and how it compares with other interpolating techniques. If the values of x are at equidistant or not at equidistant, we use Lagrange’s interpolation formula. f = the value of the function at the data (or interpolation) point i Vi x = the Lagrange basis function Each Lagrange polynomial or basis function is set up such that it equals unity at the data point with which it is associated, zero at all other data points and nonzero in-between. Lagrange interpolation is a well known, classical technique for interpolation [194]. Learn the formula using solved examples. 7yv hdhl6 mjom pw f1qx8 ftnm 2jh do2nhk nxo utxpw