The computation of spherical harmonic coefficients of the Earth’s gravity field from satellite-to-satellite tracking (SST) data and satellite gravity gradiometry (SGG) data is considered. As long as the functional model related to SST data contains nuisance parameters (e.g. unknown initial state vectors), assembling of the corresponding normal matrix must be supplied with the back-substitution ...

We propose a new method that uses deep learning techniques to accelerate the popular alternating direction method of multipliers (ADMM) solution for inverse problems. The ADMM updates consist of a proximity operator, a least squares regression that includes a big matrix inversion, and an explicit solution for updating the dual variables. Typically, inner loops are required to solve the first tw...

Geometric Dilution of Precision (GDOP) is a coefficient for constellations of Global Positioning System (GPS) satellites. These satellites are organized geometrically. Traditionally, GPS GDOP computation is based on the inversion matrix with complicated measurement equations. A new strategy for calculation of GPS GDOP is construction of time series problem; it employs machine learning and artif...

The helicopter-borne electromagnetic (HEM) frequency-domain exploration method is an airborne electromagnetic (AEM) technique that is widely used for vast and rough areas for resistivity imaging. The vast amount of digitized data flowing from the HEM method requires an efficient and accurate inversion algorithm. Generally, the inverse modelling of HEM data in the first step requires a precise a...

Extreme learning machine (ELM) as an emergent technology has shown its good performance in classification applications. However, ELM algorithm needs to find the inversion of matrix in nature, which will limit its application on many occasions. This paper proposes an ELM speedup algorithm based on the analysis of ELM algorithm. By applying randomized approximation method, the proposed algorithm ...

5 Applications of Linear Algebra 24 5.1 The Cayley-Hamilton Theorem . . . . . . . . . . . . . . . . . . . 24 5.2 Solving State Equations . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Matrix Decompositions . . . . . . . . . . . . . . . . . . . . . . . 29 5.4 Bilinear Forms and Sign-definite Matrices . . . . . . . . . . . . . 32 5.4.1 Definite Matrices . . . . . . . . . . . . . . . . . . ....