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Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and ...

Background: Students’ prior mathematical knowledge plays a critical role in their success in university mathematics, yet it is often treated diagnostically rather than instructionally. Aim: This study examines studen...

Materias / palabras clave: Mathematics; Inequality; Matrix (chemical analysis); Algebra over a field; Pure mathematics; Calculus (dental); Mathematical economics; Applied mathematics; Computer science; Mathematical analysis; Materials science; Den...

Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation. Large Sample Theory and ...

We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in...

Materias / palabras clave: Mathematics; Linear operators; Characterization (materials science); Pure mathematics; Operator theory; Algebra over a field; Applied mathematics; Mathematical analysis; Physics; Optics; Bounded function

Previous article Next article An Algorithm for Least-Squares Estimation of Nonlinear ParametersDonald W. MarquardtDonald W. Marquardthttps://doi.org/10.1137/0111030PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport Ci...

Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods...

In this book the authors present classical and recent results for matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, ...

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way array...

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathe...

A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results. The method, Dmol for short, uses fast convergent three-dimensional numerical integrati...

We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion ...

A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higher-order structure in the association of terms with documents (“semantic structure”) in order to impro...

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order...

Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functi...

Although the problem of determining the minimum cost path through a graph arises naturally in a number of interesting applications, there has been no underlying theory to guide the development of efficient search procedu...

A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunctio...

In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the ...

Contracted Gaussian basis sets for molecular calculations are derived from uncontracted (12,8) and (12,9) sets for the neutral second row atoms, Z=11–18, and for the negative ions P−, S−, and Cl−. Calculations on...

Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method for calculating semilocal pseudopotential mat...

Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self-consistent field ground state energies with respect to all basis set parameters, i.e., orbital ...