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The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems
TLDR
A unifying characterization of various regularization methods is given and it is shown that the measurement of “size” is dependent on the particular regularization method chosen, and a new method is proposed for choosing the regularization parameter based on the L-curve.
IEEE TRANSACTIONS ON SYSTEMS , MAN , AND CYBERNETICS
These results indicate that shadow detection is difficult prior to segment noise cleaning, but may be possible for the nonnoise segments. Shadows can be used to verify the recognition of segments
Multi-Splittings of Matrices and Parallel Solution of Linear Systems
TLDR
Two classes of matrix splittings are presented and applications to the parallel iterative solution of systems of linear equations are given, resulting in algorithms which can be implemented efficiently on parallel computing systems.
Regularization by Truncated Total Least Squares
TLDR
This paper proposes and test an iterative algorithm based on Lanczos bidiagonalization for computing truncated TLS solutions and expresses the results in terms of the singular value decomposition of the coefficient matrix rather than the augmented matrix, which leads to insight into the filtering properties of the truncation TLS method as compared to regularized least squares solutions.
Tikhonov Regularization and Total Least Squares
TLDR
It is shown how Tikhonov's regularization method can be recast in a total least squares formulation suited for problems in which both the coefficient matrix and the right-hand side are known only approximately.
Deblurring Images: Matrices, Spectra and Filtering
TLDR
This chapter discusses Manipulating Images in MATLAB using Structured Matrix Computations and Spectral Filtering to Regularize Color Images, Smoothing Norms, and Other Topics.
A semidiscrete matrix decomposition for latent semantic indexing information retrieval
TLDR
It is shown that SDD- based LSI does as well as SVD-based LSI in terms of document retrieval while requiring only one-twentieth the storage and one-half the time to compute each query.
Why Do Hubs in the Yeast Protein Interaction Network Tend To Be Essential: Reexamining the Connection between the Network Topology and Essentiality
TLDR
A rigorous analysis of six variants of the genomewide protein interaction network for Saccharomyces cerevisiae demonstrated that the majority of hubs are essential due to their involvement in Essential Complex Biological Modules, a group of densely connected proteins with shared biological function that are enriched in essential proteins.
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
TLDR
This work modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer iteration to produce an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200.
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