What is he best known for?
The fields of study he is best known for:
- Eigenvalues and eigenvectors
- Algebra
- Mathematical analysis
His main research concerns Eigenvalues and eigenvectors, Applied mathematics, Mathematical analysis, Lanczos algorithm and Symmetric matrix.
His studies in Eigenvalues and eigenvectors integrate themes in fields like Matrix and Combinatorics.
Beresford N. Parlett has included themes like Tridiagonal matrix algorithm and Transformation in his Lanczos algorithm study.
His study looks at the relationship between Symmetric matrix and topics such as Algorithm, which overlap with Relaxation, Rate of convergence, Runge–Kutta methods and Theoretical computer science.
In his study, QR algorithm and Arnoldi iteration is inextricably linked to Mathematical proof, which falls within the broad field of Rayleigh quotient iteration.
His Arnoldi iteration research integrates issues from Variety, EISPACK and Scope.
His most cited work include:
- The symmetric eigenvalue problem (2830 citations)
- Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations (343 citations)
- The Lanczos algorithm with selective orthogonalization (320 citations)
What are the main themes of his work throughout his whole career to date?
Eigenvalues and eigenvectors, Tridiagonal matrix, Applied mathematics, Algebra and Matrix are his primary areas of study.
He interconnects Algorithm, Symmetric matrix and Mathematical analysis in the investigation of issues within Eigenvalues and eigenvectors.
The various areas that Beresford N. Parlett examines in his Tridiagonal matrix study include Factorization, Block matrix, Combinatorics and Computation.
Beresford N. Parlett has researched Applied mathematics in several fields, including Eigenvalue perturbation, Convergence, Condition number and Defective matrix.
His Convergence study integrates concerns from other disciplines, such as QR algorithm and Hessenberg matrix.
His Matrix research is multidisciplinary, incorporating perspectives in Iterative method and Pure mathematics.
He most often published in these fields:
- Eigenvalues and eigenvectors (46.67%)
- Tridiagonal matrix (28.48%)
- Applied mathematics (21.82%)
What were the highlights of his more recent work (between 2006-2020)?
- Eigenvalues and eigenvectors (46.67%)
- Tridiagonal matrix (28.48%)
- Matrix (21.21%)
In recent papers he was focusing on the following fields of study:
Beresford N. Parlett focuses on Eigenvalues and eigenvectors, Tridiagonal matrix, Matrix, Combinatorics and Algorithm.
To a larger extent, Beresford N. Parlett studies Algebra with the aim of understanding Eigenvalues and eigenvectors.
The concepts of his Tridiagonal matrix study are interwoven with issues in Matrix splitting, Inverse iteration, Block matrix and Structure.
His work carried out in the field of Matrix brings together such families of science as Numerical analysis and Pure mathematics.
His Combinatorics research is multidisciplinary, relying on both Diagonal, Wilkinson matrix, Complex plane and Integer.
His Hybrid algorithm study, which is part of a larger body of work in Algorithm, is frequently linked to Worst-case complexity, bridging the gap between disciplines.
Between 2006 and 2020, his most popular works were:
- Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers (70 citations)
- On nonsymmetric saddle point matrices that allow conjugate gradient iterations (29 citations)
- Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers (29 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Eigenvalues and eigenvectors
- Complex number
His primary areas of investigation include Matrix, Eigenvalues and eigenvectors, Tridiagonal matrix, Symmetric matrix and Algorithm.
His research in Matrix intersects with topics in Iterative method, Numerical analysis and Conjugate gradient method.
Beresford N. Parlett studies Eigenvalues and eigenvectors, focusing on Hessenberg matrix in particular.
His Tridiagonal matrix research is multidisciplinary, incorporating elements of Range, Software and Algorithmics.
His Algorithm research incorporates elements of Matrix decomposition and Theoretical computer science.
His QR algorithm study frequently intersects with other fields, such as Inverse iteration.
This overview was generated by a machine learning system which analysed the scientist’s
body of work. If you have any feedback, you can
contact us
here.
