We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present st...

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recursive procedure admits a physical interpretation in terms of discretized transmission lines. In this framework the generating system is constru...

We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...

An approach to analyzing structures by using beam elements is developed with adaptive displacement interpolation functions. First, the element stiffness matrix and equivalent nodal loads are derived on the basis of the equilibrium between nodal forces and section forces rather than the compatibility between nodal deformations and section deformations, which avoids discretization errors caused b...

We consider problems where one seeks m×m matrix valued H∞ functions w(ξ) which satisfy interpolation constraints and a bound (0.1) w∗(ξ)w(ξ) ≤ ρmin, |ξ| < 1, where the m×m positive semi-definite matrix ρmin is minimal (no smaller than) any other matrix ρ producing such a bound. That is, if (0.2) w∗(ξ)w(ξ) ≤ ρ, |ξ| < 1, and if ρmin − ρ is positive semi-definite, then ρmin = ρ. This is an example...

We propose a new algorithm to improve computational efficiency for low rank based interpolation. The interpolation is carried out in the frequency spatial domain where each frequency slice is first transferred to the frequency-patches domain. A nice feature of this domain is that the number of non-zero singular values can be better related to seismic events, which favors low rank reduction. Dur...

We consider the nonlinear matrix equation X = Q+A (I⊗X−C)A (0 < δ ≤ 1), where Q is an n× n positive definite matrix, C is an mn×mn positive semidefinite matrix, I is the m×m identity matrix, and A is an arbitrary mn×n matrix. We prove the existence and uniqueness of the solution which is contained in some subset of the positive definite matrices under the condition that I ⊗Q > C. Two bounds for...

Constructing a propagation map from set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance regions with very sparse measurements. Recent advance matrix completion has the potential to reconstruct measurements, but spatial resolution is limited. This paper propo...