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Articles 1 - 6 of 6
Full-Text Articles in Other Applied Mathematics
The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane
The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane
Dissertations, Master's Theses and Master's Reports
Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L2(M) → X, U : L2(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that
T = UmσV †,
with mσ : L2(M ) → L2(M ) defined by mσ(f ) = σf for all f …
Sub-Sampled Matrix Approximations, Joy Azzam
Sub-Sampled Matrix Approximations, Joy Azzam
Dissertations, Master's Theses and Master's Reports
Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate a matrix A with an appropriate embedding of the data sampled. This work introduces a novel family of randomized iterative algorithms which use significantly less data per iteration than current methods by sampling input and output spaces simultaneously. The data footprint of the algorithms can be tuned (independent of the underlying matrix dimension) to available hardware. Proof is given for the convergence of the algorithms, which are referred to as sub-sampled, in terms of numerically tested …
Credit Risk Analysis Using Machine Learning And Neural Networks, Dhruv Dhanesh Thanawala
Credit Risk Analysis Using Machine Learning And Neural Networks, Dhruv Dhanesh Thanawala
Dissertations, Master's Theses and Master's Reports
A key activity within the banking industry is to extend credit to customers, hence,
credit risk analysis is critical for nancial risk management. There are various methods
used to perform credit risk analysis. In this project, we analyze German and
Australian nancial data from UC Irvine Machine Learning repository, reproducing
results previously published in literature. Further, using the same dataset and various
machine learning algorithms, we attempt to create better models by tuning available
parameters, however, our results are at best comparable to published results.
In this report, we have explained the algorithms and mathematical framework that
goes behind developing …
Evaporation Of A Sessile Droplet On A Slope, Mitch Timm
Evaporation Of A Sessile Droplet On A Slope, Mitch Timm
Dissertations, Master's Theses and Master's Reports
We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from a purely diffusive transport of the liquid vapor and that the contact line is a pinned circle. For the purposes of our analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the …
Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig
Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig
Dissertations, Master's Theses and Master's Reports
Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on Rd, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer.
In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, …
Evaluating The Long-Term Effects Of Logging Residue Removals In Great Lakes Aspen Forests, Michael I. Premer
Evaluating The Long-Term Effects Of Logging Residue Removals In Great Lakes Aspen Forests, Michael I. Premer
Dissertations, Master's Theses and Master's Reports
Commercial aspen (Populus spp.) forests of the Great Lakes region are primarily managed for timber products such as pulp fiber and panel board, but logging residues (topwood and non-merchantable bolewood) are potentially important for utilization in the bioenergy market. In some regions, pulp and paper mills already utilize residues as fuel in combustion for heat and electricity, and progressive energy policies will likely cause an increase in biomass feedstock demand. The effects of removing residues, which have a comparatively high concentration of macronutrients, is poorly understood when evaluating long-term site productivity, future timber yields, plant diversity, stand dynamics, and …