Beresford Parlett

Beresford Parlett's AcademicInfluence.com Rankings

Beresford Parlett

Mathematics

#3682

World Rank

#5387

Historical Rank

Applied Mathematics

#119

World Rank

#134

Historical Rank

Measure Theory

#799

World Rank

#1062

Historical Rank

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Mathematics

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According to Wikipedia, Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation. Education and career Parlett received in 1955 his bachelor's degree in mathematics from the University of Oxford and then worked in his father's timber business for three years. From 1958 to 1962 he was a graduate student in mathematics at Stanford University, where he received his Ph.D. in 1962. He was a postdoc for two years at Manhattan's Courant Institute and one year at the Stevens Institute of Technology. From 1965 until his retirement, he was a faculty member of the mathematics department at the University of California, Berkeley. There he served for some years as chair of the department of computer science, director of the Center for Pure and Applied Mathematics, and professor in the department of electrical engineering and computer science. He was a visiting professor at the University of Toronto, Pierre and Marie Curie University , and the University of Oxford.

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Beresford Parlett's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Symmetric Eigenvalue Problem (1981) (3810)
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations (1971) (424)
The Lanczos algorithm with selective orthogonalization (1979) (411)
On generalized successive overrelaxation methods for augmented linear systems (2005) (368)
A Look Ahead Lanczos Algorithm for Unsymmetric Matrices (1985) (338)
Approximate solutions and eigenvalue bounds from Krylov subspaces (1995) (324)
Accurate singular values and differential qd algorithms (1994) (240)
The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices (1974) (201)
Balancing a matrix for calculation of eigenvalues and eigenvectors (1969) (180)
Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices (2004) (163)
Orthogonal Eigenvectors and Relative Gaps (2003) (148)
Reduction to Tridiagonal Form and Minimal Realizations (1992) (144)
A new look at the Lanczos algorithm for solving symmetric systems of linear equations (1980) (135)
The design and implementation of the MRRR algorithm (2006) (123)
Residual Bounds on Approximate Eigensystems of Nonnormal Matrices (1982) (113)
A recurrence among the elements of functions of triangular matrices (1976) (113)
An American National Standard- IEEE Standard for Binary Floating-Point Arithmetic (1985) (102)
Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers (2008) (102)
On estimating the largest eigenvalue with the Lanczos algorithm (1982) (100)
Decomposition of a symmetric matrix (1976) (95)
Laguerre's Method Applied to the Matrix Eigenvalue Problem (1964) (93)
Relatively robust representations of symmetric tridiagonals (2000) (91)
A geometric theory for the QR, LU and power iterations. (1973) (90)
Lanczos versus subspace iteration for solution of eigenvalue problems (1983) (88)
How to implement the spectral transformation (1987) (85)
Fernando's solution to Wilkinson's problem: An application of double factorization (1997) (85)
The New qd Algorithms (1995) (76)
The QR algorithm (2000) (70)
Complex shift and invert strategies for real matrices (1987) (70)
An implementation of the dqds algorithm (positive case) (2000) (69)
Topological lines in 3D tensor fields and discriminant Hessian factorization (2005) (61)
The Algebraic Eigenvalue Problem (J. H. Wilkinson) (1966) (60)
Tracking the Progress of the Lanczos Algorithm for Large Symmetric Eigenproblems (1981) (60)
Global convergence of the basic algorithm on Hessenberg matrices (1968) (58)
The Symmetric Eigenvalue Problem (Classics in Applied Mathematics, Number 20) (1999) (54)
Use of indefinite pencils for computing damped natural modes (1990) (51)
Block reflectors: theory and computation (1988) (50)
Methods for Scaling to Doubly Stochastic Form (1982) (49)
Can There Be a Marriage Function (1972) (49)
Element Preconditioning Using Splitting Techniques (1985) (49)
The use of a refined error bound when updating eigenvalues of tridiagonals (1985) (46)
Ergodic properties of populations. I. The one sex model. (1970) (42)
On nonsymmetric saddle point matrices that allow conjugate gradient iterations (2008) (40)
Topological structures of 3D tensor fields (2005) (38)
Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers (2008) (36)
Accurate Computation of Divided Differences of the Exponential Function (1984) (35)
Forward instability of tridiagonal QR (1993) (34)
HOW FAR SHOULD YOU GO WITH THE LANCZOS PROCESS (1976) (32)
A new proof of global convergence for the tridiagonal QL algorithm (1977) (32)
The Software Scene in the Extraction of Eigenvalues from Sparse Matrices (1984) (32)
Analysis of Algorithms for Reflections in Bisectors (1971) (31)
On the convergence of a practical QR algorithm (1968) (31)
The Transformation of Second-Order Linear Systems into Independent Equations (2011) (31)
Prospectus for the Next LAPACK and ScaLAPACK Libraries (2006) (29)
Application of a New Algorithm for the Symmetric Eigenproblem to Computational Quantum Chemistry (1997) (29)
Towards a black box Lanczos program (1989) (29)
MULTIPLE REPRESENTATIONS: (1998) (27)
A Newton-Lanczos method for solution of non-linear finite element equations (1983) (27)
Invariant subspaces for tightly clustered eigenvalues of tridiagonals (1996) (26)
Glued Matrices and the MRRR Algorithm (2005) (26)
The (matrix) discriminant as a determinant (2002) (25)
Implicit Cholesky algorithms for singular values and vectors of triangular matrices (1993) (24)
Matrices with prescribed Ritz values (2008) (24)
Multi-Scale Spectral Decomposition of Massive Graphs (2014) (21)
Canonical decomposition of Hessenberg matrices (1967) (19)
Computation of Functions of Triangular Matrices. (1974) (19)
Refined Interlacing Properties (1992) (19)
Symmetric matrix pencils (1991) (19)
The Influence of the Compiler on the Cost of Mathematical Software—in Particular on the Cost of Triangular Factorization (1975) (18)
LINPACK Users’ Guide (J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W. Stewart) (1981) (18)
Development of an Accurate Algorithm for EXP(Bt). Appendix (1985) (17)
Semi-duality in the two-sided lanczos algorithm (1993) (17)
A Fast Solver Free of Fill-In for Finite Element Problems (1982) (16)
Progress in Numerical Analysis (1978) (15)
From qd to LR, or, how were the qd and LR algorithms discovered? (2011) (14)
Detecting Localization in an Invariant Subspace (2011) (14)
Computations of eigenpair subsets with the MRRR algorithm (2006) (14)
Global Convergence of the Basic QR Algorithm (2016) (14)
Spectral sensitivity of products of bidiagonals (1998) (13)
For tridiagonals T replace T with LDL t (2000) (12)
The contribution of J. H. Wilkinson to numerical analysis (1990) (11)
Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix (2012) (11)
Do We Fully Understand the Symmetric Lanczos Algorithm Yet (1995) (9)
Winograd's fourier transform via circulants (1982) (8)
A Bidiagonal Matrix Determines Its Hyperbolic SVD to Varied Relative Accuracy (2005) (8)
Normal Hessenberg and moment matrices (1973) (8)
Some basic information on information-based complexity theory (1992) (8)
Convergence of LR algorithm for a one-point spectrum tridiagonal matrix (2009) (8)
An Analysis of Lanczos Algorithms for Symmetric Matrices (1974) (8)
Perturbation of Eigenpairs of Factored Symmetric Tridiagonal Matrices (2003) (7)
The Spectrum of a Glued Matrix (2009) (7)
Eigenvector matrices of symmetric tridiagonals (1984) (7)
A result complementary to Gersgorin's Circle Theorem (2009) (6)
Diagonal Scaling to an Orthogonal Matrix (1981) (6)
The Construction of Orthogonal Eigenvectors for Tight Clusters by Use of Submatrices (1996) (6)
LAPACK WORKING NOTE 167: SUBSET COMPUTATIONS WITH THE MRRR ALGORITHM (2005) (6)
Very Early Days of Matrix Computations (2003) (6)
A TESTING INFRASTRUCTURE FOR LAPACK ’ S SYMMETRIC EIGENSOLVERS (2007) (6)
Algorithm 517: A Program for Computing the Condition Numbers of Matrix Eigenvalues Without Computing Eigenvectors [F2] (1977) (6)
A note on La Budde’s algorithm (1964) (5)
The uniform convergence of matrix powers (1966) (5)
Programs to Swap Diagonal Blocks (1987) (5)
Correction to convergence of the QR algorithm (1967) (5)
A Program to Compute the Condition Numbers of Matrix Eigenvalues without Computing Eigenvectors. (1975) (5)
Can You Count on Your Calculator. (1977) (5)
Singular and invariant matrices under the $QR$ transformation (1966) (5)
Another orthogonal matrix (2006) (5)
Explicit construction of hyperdominant symmetric matrices with assigned spectrum (1997) (5)
What Hadamard Missed (1996) (5)
The Inverse Eigenvector Problem for Real Tridiagonal Matrices (2016) (4)
A Way to Find the Most Redundant Equation in a Tridiagonal System (1995) (4)
Use of an Indefinite Inner Product for Computing Damped Natural Modes (1988) (4)
APPLICATIONS OF LAGUERRE'S METHOD TO THE MATRIX EIGENVALUE PROBLEM (1962) (4)
LAPACK WORKING NOTE 163 : HOW THE MRRR ALGORITHM CAN FAIL ON TIGHT EIGENVALUE CLUSTERS (2004) (3)
The Development and Use of Methods of Lr Type (2015) (3)
Linear algebra meets Lie algebra: the Kostant-Wallach theory (2008) (3)
On the Forward Instability of the QR Transformation (1988) (3)
BIT Numerical Mathematics: Editorial (2005) (3)
Effect of the CYBER 205 on Methods for Computing Natural Frequencies of Structures (1984) (2)
Accuracy and dissipation in difference schemes (2010) (2)
Computing Extremal Singular Triplets of Sparse Matrices on a Shared-Memory Multiprocessor (1994) (2)
The spectral diameter as a function of the diagonal entries (2003) (2)
Convergence of the Qr Algorithm (2017) (2)
Minimum Eigenvalue Separation (1992) (2)
A note on communication analysis of parallel sparse Cholesky factorization on a hypercube (1990) (2)
Differential qd algorithms (1993) (2)
QR; Its Forward Instability and Failure to Converge (1991) (2)
Matrix Eigenvalue Problems (1965) (2)
Numerical computations: its nature and research directions (1979) (2)
Real dqds for the nonsymmetric tridiagonal eigenvalue problem (2012) (2)
Prospectus for a Dense Linear Algebra Software Library (2007) (2)
The method of minimal representations in 2D using model calculations (1994) (2)
Fifth SIAM conference on applied linear algebra. Final report (1994) (1)
Eigenpairs of Wilkinson Matrices (2020) (1)
The accurate solution of eigenvalue problems (2000) (1)
Review: Herman H. Goldstine, A history of numerical analysis from the 16th through the 19th century (1979) (1)
The State-of-the-Art in Extracting Eigenvalues and Eigenvectors in Structural Mechanics, (1987) (1)
13. Lanczos Algorithms (1998) (1)
A Program to Compute the Real Schur Form of a Real Square Matrix. (1975) (1)
Notes on the number of multiplications required to form the product of two N × N matrices (1969) (1)
Necessary and sufficient conditions for convergence of the QR algorithm on Hessenberg matrix (1966) (1)
The Lanczos Algorithm with Implicit Deflation. (1977) (1)
The Influence of the Compiler on the Cost of Triangular Factorization. (1973) (1)
8. The QL and QR Algorithms (1998) (1)
Large Sparse Sets of Linear Equations (J. K. Reid, ed.); Sparse Matrices and Their Applications (Donald J. Rose and Ralph A. Willoughby, ed.) (1974) (1)
Implementation Of Lanczos Algorithms on Vector Computers (1985) (1)
Implementation of Minimal Representations in 2d Ising Model Calculations (1992) (0)
2. Tasks, Obstacles, and Aids (1998) (0)
1. Basic Facts about Self-Adjoint Matrices (1998) (0)
A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem (2022) (0)
REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS (2016) (0)
CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX (2008) (0)
How to Solve (K - lambda M)z = O for Large K and M, (1981) (0)
10. Eigenvalue Bounds (1998) (0)
A Matrix Eigenvalue Problem (G. Efroymson, A. Steger and S. Steinberg) (1981) (0)
Roundoff Error in the Solution of Finite Element Systems (1976) (0)
A Program to Calculate Solutions and Error Bounds to Finite Interval Sturm-Lioville Eigenvalue Problems. (1971) (0)
11. Approximations from a Subspace (1998) (0)
15. The General Linear Eigenvalue Problem (1998) (0)
Numerical Methods. vols. 1 and 2. vol. 1, Iteration, Programming, and Algebraic Equations (168 pp., $3); vol. 2, Differences, Integration, and Differential Equations (224 pp., $2.75). Ben Noble. Oliver and Boyd, London; Interscience (Wiley), New York, 1965 (1965) (0)
J. H. Wilkinson's work and influence on matrix computations (1987) (0)
BUNDLES OF MATRICES AND THE LINEAR INDEPENDENCE OF THEIR MINORS (1961) (0)
Convergence of the Q-R algorithm for Hessenberg matrices (1966) (0)
SENSITIVITY OF EIGENVALUES OF AN UNSYMMETRIC TRIDIAGONAL (2012) (0)
4. Simple Vector Iterations (1998) (0)
Contribution II/11 Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors* (1971) (0)
Convergence of theQR algorithm (1965) (0)
Nearly minimal reduced order systems (1997) (0)
Revelations of a transposition matrix (2010) (0)
The Discrete Fourier Transform via Circulants. (1980) (0)
3. Counting Eigenvalues (1998) (0)
Analytic Complexity Theory and the Solution of Ax=b, (1981) (0)
9. Jacobi Methods (1998) (0)
Book ReviewReview of Functions of Matrices: Theory and Computation, Nicholas J. Higham. SIAM, Philadelphia, PA (2008), xx + 425 pp. (2009) (0)
Communication Cost of Sparse Cholesky Factorization on a Hypercube (1988) (0)
Research in Efficient Scientific Computation (1992) (0)
Eigenvalues, anyone? (1967) (0)
The Largest Eigenvalue of a Positive Definite Symmetric Matrix: 10839 (2002) (0)
7. Tridiagonal Form (1998) (0)
A fast stable algorithm for frequency response problems (1996) (0)
Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix (2012) (0)
Frequency response plots : New approaches (1996) (0)
International Workshop on the Accurate Solution of Eigenvalue Problems (IWASEP IV) (2006) (0)
Low-Rank Update Eigensolver for Supercell Band Structure Calculations (2001) (0)
Lanczos Algorithm Applied to Modal Analysis of Very Large Structures. (1985) (0)
Singular Vectors via Differential qd (1995) (0)
Decomposition of a Symmetric Matrix ; CU-CS-080-75 (1975) (0)
6. Useful Orthogonal Matrices (Tools of the Trade) (1998) (0)

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Published Works

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What Schools Are Affiliated With Beresford Parlett?

Beresford Parlett's AcademicInfluence.com Rankings