Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

linalg::vandermonde

Vandermonde matrix

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

Syntax

linalg::vandermonde([v1, v2, …], <R>)

Description

linalg::vandermonde(v1, v2, ... , vn) returns the n×n Vandermonde matrix V with entries Vij = vij - 1.

Use linalg::vandermonde([v1, ..., vn], R) to define the n×n Vandermonde matrix over the field R. Note that the Vandermonde nodes vi must be elements of R or must be convertible to elements of R.

Vandermonde matrices of dimension n×n can be inverted with O(n2) operations. Linear equations with a Vandermonde coefficient matrix can be solved via linalg::vandermondeSolve.

Examples

Example 1

Create a 3×3 Vandermonde matrix:

V := linalg::vandermonde([v1, v2, v3])

V is a matrx of the domain Dom::Matrix().

domtype(V)

You can specify a special component ring for the matrices, provided the nodes can be converted to elements of the ring. For example, specification of the domain Dom::Float generates floating-point entries:

V := linalg::vandermonde([2, PI, 1/3], Dom::Float)

domtype(V)

delete V

Parameters

v1, v2, …

The Vandermonde nodes: arithmetical expressions

R

The component ring: a domain of category Cat::Rng; default: Dom::ExpressionField()

Return Values

n×n matrix of the domain Dom::Matrix(R).

Algorithms

Vandermonde matrices are notoriously ill-conditioned. The inverses of large floating-point Vandermonde matrices are subject to severe round-off effects.

Was this topic helpful?