The first Section below extends to m × n matrices the results on orthogonality and projection we have previously seen for vectors. The Sections thereafter use these concepts to introduce the Singular Value Decomposition (SVD) of a matrix, the pseudo-inverse, and its use for the solution of linear systems.

We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a polynomial approximation scheme using Chebyshev polynomials, Chebyshev grids, and low rank function approximation. Numerical experiments demonstrate that our ...

— We introducé abstract interpolating sphnes of minimum norm by using the concept of restncted pseudo-inverse ofMinamide and Nakamura We propose a certain invariance relation which generahzes the Golomb-Weinberger-Sard method As an application we considei abstract tensor product sphnes.

Building visual recognition models that adapt across different domains is a challenging task for computer vision. While feature-learning machines in the form of hierarchial feed-forward models (e.g., convolutional neural networks) showed promise in this direction, they are still difficult to train especially when few training examples are available. In this paper, we present a framework for tra...

In this paper, a simple inverse structure for multichannel active noise control (ANC) is introduced, based on the use of noncausal models of the (pseudo-)inverse plant between the error sensors (typically microphones in ANC systems) and the actuators (typically loudspeakers). This structure, combined with adaptive FIR filters and filtered-x LMS-based algorithms, can produce both a reduction of ...

In this paper, we introduce two classes of localized integral operators on L2(Rd) with the Wiener class W and the Kurbatov class K of integral operators as their models. We show that those two classes of localized integral operators are pseudo-inverse closed non-unital subalgebra of B2, the Banach algebra of all bounded operators on L2(Rd) with usual operator norm.

This paper proposes a method to accommodate multiple tasks for redundancy utilization, which is based on a specific weighted pseudo-inverse. The proposed method also has task priority imposition property as those conventional task priority based method. In order to deal with general situations of task specification, the so-called semi-definitely weighted pseudoinverse is devised.

Layered space-time codes have been designed to exploit the capacity advantage of multiple antenna systems in Rayleigh fading environments. In this paper, a new efficient decoding algorithm based on QR decomposition is presented. It needs only a fraction of computational effort compared to the standard decoding algorithm requiring the multiple calculation of the pseudo inverse of the channel mat...

We present an alternative to the pseudo-inverse method for determining the hidden to output weight values for Extreme Learning Machines performing classification tasks. The method is based on linear discriminant analysis and provides Bayes optimal single point estimates for the weight values.

Ensemble Kalman inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems (Iglesias et al. Inverse Probl 29: 045001, 2013). It samples particles from prior distribution and introduces motion to move the around pseudo-time. As pseudo-time goes infinity, method finds minimizer of objective function, when stops at 1, ensemble resembles, some sense, posterior linear settin...