  We extend the softFEM idea to isogeometric analysis (IGA) to reduce the
stiffness (consequently, the condition numbers) of the IGA discretized problem.
We refer to the resulting approximation technique as softIGA. We obtain the
resulting discretization by first removing the IGA spectral outliers to reduce
the system's stiffness. We then add high-order derivative-jump penalization
terms (with negative penalty parameters) to the standard IGA bilinear forms.
The penalty parameter seeks to minimize spectral/dispersion errors while
maintaining the coercivity of the bilinear form. We establish dispersion errors
for both outlier-free IGA (OF-IGA) and softIGA elements. We also derive
analytical eigenpairs for the resulting matrix eigenvalue problems and show
that the stiffness and condition numbers of the IGA systems significantly
improve (reduce). We prove a superconvergent result of order $h^{2p+4}$ for
eigenvalues where $h$ characterizes the mesh size and $p$ specifies the order
of the B-spline basis functions. To illustrate the main idea and derive the
analytical results, we focus on uniform meshes in 1D and tensor-product meshes
in multiple dimensions. For the eigenfunctions, softIGA delivers the same
optimal convergence rates as the standard IGA approximation. Various numerical
examples demonstrate the advantages of softIGA over IGA.
