# homogeneous polynomial

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## homogeneous polynomial

[‚hä·mə′jē·nē·əs ‚päl·ə′nō·mē·əl]
(mathematics)
A polynomial all of whose terms have the same total degree; equivalently it is a homogenous function of the variables involved.
References in periodicals archive ?
We can therefore reject the hypothesis that students will master inverse demand if they are given enough time; rather surprisingly, they do better with novel homogeneous forms that they've never used.
In the next section we will apply Newton to the homogeneous form of (1.2) and derive a new correction equation for Jacobi-Davidson for the quadratic eigenproblem.
Suppose we have an approximate eigenvector u [approximate equal to] x of unit length and a corresponding approximate eigenvalue [theta] := [alpha]/[beta] [approximately equal to] [lambda] in homogeneous form, where [alpha]/[beta] is the Rayleigh quotient of u and satisfies
The fact that [alpha]/[beta] is in homogeneous form means that [alpha] and [beta] can still be simultaneously scaled by a nonzero scalar; it is their ratio that matters.
Our ansatz is to find an update for both the approximate eigenvalue (in homogeneous form) ([alpha], [beta]) and the approximate eigenvector u: we look for ([DELTA][alpha], [DELTA][beta]) [perpendicular to] ([alpha], [beta]) and s [perpendicular to] u such that

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