A general interpolation method for symmetric second-rank tensors in two dimensions

A new interpolation method for 2 x 2 symmetric second-rank tensors is proposed. It uses a vector representation of tensors using its eigenvalues and the rotation angle of the major eigenvector with respect to a cartesian coordinate system. These characteristics are then linearly interpolated. Although it is not constricted to positive definite tensors, it preserves this property for tensors with nonnegative eigenvalues. We compare this technique with the matrix coefficient linear in terpolation. The experiments show that our technique improves the results.