Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the 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?