  A new class of affine scaling matrices for the interior point Newton-type
methods is considered to solve the nonlinear systems with simple bounds. We
review the essential properties of a scaling matrix and consider several
well-known scaling matrices proposed in the literature. We define a new scaling
matrix that is the convex combination of these matrices. The proposed scaling
matrix inherits those interesting properties of the individual matrices and
satisfies additional desired requirements. The numerical experiments
demonstrate the superiority of the new scaling matrix in solving several
important test problems.
