Results 1 to 10 of about 34,257 (101)
Bidiagonal Decompositions and Accurate Computations for the Ballot Table and the Fibonacci Matrix
Numerical Linear Algebra With ApplicationsABSTRACT Riordan arrays include many important examples of matrices. Here we consider the ballot table and the Fibonacci matrix. For finite truncations of these Riordan arrays, we obtain bidiagonal decompositions. Using them, algorithms to solve key linear algebra problems for ballot tables and Fibonacci matrices with high relative accuracy are derived.
Juan Manuel Pena +2 more
exaly +4 more sources
Bidiagonal Decompositions and High‐Accuracy Computations for Newton Collocation Matrices
Numerical Linear Algebra With ApplicationsABSTRACT We consider a class of collocation matrices A$$ A $$ associated with the Newton basis of the space of polynomials of degree at most n$$ n $$, evaluated at a set of l+1≥n+1$$ l+1\ge n+1 $$ nodes. In the most general setting, we allow n$$ n $$ of these nodes to either coincide with or differ from those defining the Newton basis.
Esmeralda Mainar
exaly +3 more sources
Bidiagonal Factorizations of Filbert and Lilbert Matrices [PDF]
AxiomsExtensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices.
Beatriz Rubio-Serrano +2 more
exaly +4 more sources
EFAMIX, a tool to decompose inline chromatography SAXS data from partially overlapping components. [PDF]
Protein Sci, 2022 Abstract Small‐angle X‐ray scattering (SAXS) is an established technique for structural analysis of biological macromolecules in solution. During the last decade, inline chromatography setups coupling SAXS with size exclusion (SEC‐SAXS) or ion exchange (IEC‐SAXS) have become popular in the community.
Konarev PV +6 more
europepmc +2 more sources
On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
doaj +1 more source
Total positivity and accurate computations with Gram matrices of Said‐Ball bases
Numerical Linear Algebra with Applications, Volume 30, Issue 6, December 2023., 2023 Abstract In this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained.
E. Mainar, J. M. Peña, B. Rubio
wiley +1 more source
Journal of Chemometrics, Volume 37, Issue 10, October 2023., 2023 Abstract In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR) may often provide efficient low‐dimensional model solutions. In unsupervised situations, the same may be true for principal component analysis (PCA).
Joakim Skogholt +4 more
wiley +1 more source
High relative accuracy with some special matrices related to Γ and β functions
Numerical Linear Algebra with Applications, Volume 30, Issue 5, October 2023., 2023 Abstract For some families of totally positive matrices using Γ$$ \Gamma $$ and β$$ \beta $$ functions, we provide their bidiagonal factorization. Moreover, when these functions are defined over integers, we prove that the bidiagonal factorization can be computed with high relative accuracy and so we can compute with high relative accuracy their ...
Jorge Delgado, Juan Manuel Peña
wiley +1 more source
Geophysical Prospecting, Volume 71, Issue 5, Page 847-875, June 2023., 2023 Abstract Non‐linear inversion of controlled source electromagnetic data is non‐unique. Inversion ambiguity and uncertainty grow with model complexity and limitations in sensitivity, for example when imaging deep targets. Uncertainties should be estimated. The best way to do that is by statistical inversion techniques.
Emmanuel Causse
wiley +1 more source
Depth of almost strictly sign regular matrices
Mathematical Methods in the Applied Sciences, Volume 46, Issue 1, Page 732-744, 15 January 2023., 2023 The concept of depth of an almost strictly sign regular matrix is introduced and used to simplify some algorithmic characterizations of these matrices.
Pedro Alonso +3 more
wiley +1 more source