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Recent Developments in Dense Numerical Linear Algebra (2000)  (Make Corrections)  
Nicholas J. Higham



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Abstract: We survey recent developments in dense numerical linear algebra, covering linear systems, least squares problems and eigenproblems. Topics considered include the design and analysis of block, partitioned and parallel algorithms, condition number estimation, componentwise error analysis, and the computation of practical error bounds. Frequent reference is made to LAPACK, the state of the art package of Fortran software designed to solve linear algebra problems efficiently and accurately on ... (Update)

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BibTeX entry:   (Update)

@techreport{ higham96recent,
    author = "Nicholas J. Higham",
    title = "Recent Developments in Dense Numerical Linear Algebra",
    number = "No. 288",
    address = "Manchester, England",
    pages = "26",
    year = "1996",
    url = "citeseer.ist.psu.edu/higham00recent.html" }
Citations (may not include all citations):
387   A set of Level 3 basic linear algebra subprograms (context) - Dongarra, Croz et al. - 1990
258   Golub and Charles F (context) - Gene - 1989
248   Solving Linear Systems on Vector and Shared Memory Computers (context) - Dongarra, Duff et al. - 1991
245   An extended set of Fortran basic linear algebra subprograms:.. - Dongarra, Croz et al. - 1988
245   An extended set of Fortran basic linear algebra subprograms - Dongarra, Croz et al. - 1988
155   Society for Industrial and Applied Mathematics (context) - Anderson, Bai et al. - 1995
126   Numerical Methods for Least Squares Problems (context) - Bjorck - 1996
102   Jacobi's method is more accurate than QR - Demmel, Veseli'c - 1992
99   Society for Industrial and Applied Mathematics (context) - Higham, Stability et al. - 1996
83   Institute of Electrical and Electronics Engineers (context) - for, Arithmetic et al. - 1987
81   Accurate singular values of bidiagonal matrices - Demmel, Kahan - 1990
79   Software libraries for linear algebra computations on high p.. - Dongarra, Walker - 1995
76   Parallel numerical linear algebra - Demmel, Heath et al. - 1993
73   Parallel algorithms for dense linear algebra computations (context) - Gallivan, Plemmons et al. - 1990
72   Sparse matrices in MATLAB: Design and implementation - Gilbert, Moler et al. - 1992
68   Design of a parallel nonsymmetric eigenroutine toolbox - Bai, Demmel - 1994
68   Design of a parallel nonsymmetric eigenroutine toolbox - Bai, Demmel - 1993
67   Matrix Eigensystem Routines---EISPACK Guide Extension (context) - Garbow, Boyle et al. - 1977
64   Rank revealing QR factorizations (context) - Chan - 1987
62   Manchester Centre for Computational Mathematics (context) - Higham, LAPACK et al. - 1995
61   A divide and conquer method for the symmetric tridiagonal ei.. (context) - Cuppen - 1981
57   Some stable methods for calculating inertia and solving symm.. (context) - Bunch, Kaufman - 1977
57   Society for Industrial and Applied Mathematics (context) - Dongarra, Bunch et al. - 1979
56   The WY representation for products of Householder matrices (context) - Bischof, Van Loan - 1987
52   Wavelet-like bases for the fast solution of second-kind inte.. (context) - Alpert, Beylkin et al. - 1993
52   Some modified matrix eigenvalue problems (context) - Golub - 1973
50   Block reduction of matrices to condensed forms for eigenvalu.. - Dongarra, Hammarling et al. - 1989
47   Fast parallel matrix inversion algorithms (context) - Csanky - 1976
46   Rankone modification of the symmetric eigenproblem (context) - Bunch, Nielsen et al. - 1978
45   Inverse free parallel spectral divide and conquer algorithms.. - Bai, Demmel et al. - 1994
44   Direct methods for solving symmetric indefinite systems of l.. (context) - Bunch, Parlett - 1971
44   Accurate singular values and differential qd algorithms (context) - Fernando, Parlett - 1994
41   a block implementation of Hessenberg multishift QR iteration (context) - Bai, Demmel - 1989
39   FORTRAN codes for estimating the one-norm of a real or compl.. (context) - Higham - 1988
34   Implementing linear algebra algorithms for dense matrices on.. (context) - Dongarra, Gustavson et al. - 1984
31   Condition estimates (context) - Hager - 1984
28   Accurate symmetric indefinite linear equation solvers (context) - Ashcraft, Grimes et al. - 1995
28   An estimate for the condition number of a matrix (context) - Cline, Moler et al. - 1979
27   Parallelizing the QR algorithm for the unsymmetric algebraic.. - Henry, Geijn - 1996
23   Stability of block algorithms with fast level-3 BLAS - Demmel, Higham - 1992
22   On swapping diagonal blocks in real Schur form (context) - Bai, Demmel - 1993
21   The bidiagonal singular value decomposition and Hamiltonian .. - Deift, Demmel et al. - 1991
20   Using Strassen's algorithm to accelerate the solution of lin.. (context) - Bailey, Lee et al. - 1991
18   Iterative refinement implies numerical stability (context) - Jankowski, Wo'zniakowski - 1977
18   Oak Ridge National Laboratory (context) - Choi, Dongarra et al. - 1994
17   Rank and null space calculations using matrix decomposition .. (context) - Foster - 1986
17   A parallel algorithm for the nonsymmetric eigenvalue problem (context) - Dongarra, Sidani - 1993
17   Stability of methods for matrix inversion - Croz, Higham - 1992
17   Stability analysis of the method of seminormal equations for.. (context) - Bjorck - 1987
16   Efficient algorithms for computing a strong rank-revealing Q.. (context) - Gu, Eisenstat - 1996
16   The sign matrix and the separation of matrix eigenvalues (context) - Howland - 1983
15   Loss and recapture of orthogonality in the modified Gram--Sc.. (context) - Bjorck, Paige - 1992
15   the augmented system approach to sparse least-squares proble.. (context) - Arioli, Duff et al. - 1989
15   A stable and efficient algorithm for the rank-one modificati.. (context) - Gu, Eisenstat - 1994
14   Stability of the diagonal pivoting method with partial pivot.. - Higham - 1995
14   A stable variant of the secant method for solving nonlinear .. (context) - Gragg, Stewart - 1976
13   Large growth factors in Gaussian elimination with pivoting (context) - Higham, Higham - 1989
13   A parallel algorithm for computing the singular value decomp.. (context) - Jessup, Sorensen - 1994
13   Accurate eigenvalues of a symmetric tri-diagonal matrix (context) - Kahan
13   Trading off parallelism and numerical stability - Demmel - 1993
12   Numerical Linear Algebra with Applications (context) - Demmel, Higham et al. - 1995
11   On Jacobi methods for singular value decompositions (context) - Hari, Veseli'c - 1987
11   A divide-and-conquer algorithm for the bidiagonal SVD (context) - Gu, Eisenstat - 1995
11   Matrix Anal (context) - note - 1991
11   Computing the generalized singular value decomposition - Bai, Demmel - 1993
11   Department of Computer Science (context) - Dongarra, Hammarling et al. - 1995
10   On growth in Gaussian elimination with complete pivoting (context) - Gould - 1991
10   On computing condition numbers for the nonsymmetric eigenpro.. (context) - Bai, Demmel et al. - 1993
9   Bounding the subspaces from rank revealing two-sided orthogo.. (context) - Fierro, Bunch - 1995
9   Gaussian elimination with partial pivoting can fail in pract.. (context) - Foster - 1994
8   Open problems in numerical linear algebra (context) - Demmel - 1992
7   Implicit Cholesky algorithms for singular values and vectors.. (context) - Fernando, Parlett - 1995
7   the correctness of some bisection-like parallel eigenvalue a.. - Demmel, Dhillon et al. - 1995
6   On designing portable high performance numerical libraries (context) - Demmel, Dongarra et al. - 1992
6   An algorithm and a stability theory for downdating the ULV d.. (context) - Barlow, Yoon et al. - 1996
6   How the QR algorithm fails to converge and how to fix it - Day - 1996
5   Rank-revealing QR factorizations and the singular value deco.. (context) - Hong, Pan - 1991
5   Stability of parallel triangular system solvers - Higham - 1995
5   Solution of augmented linear systems using orthogonal factor.. (context) - Bjorck, Paige - 1994
4   Generalizations of the singular value and QR decompositions - De Moor, Van Dooren - 1992
4   Extensions and applications of the Householder algorithm for.. (context) - Hanson, Lawson - 1969
4   High performance linear algebra users' guide (context) - Dongarra, Pozo et al. - 1995
4   An efficient rank detection procedure for modifying the ULV .. (context) - Barlow, Yoon - 1995
4   A case against a divide and conquer approach to the nonsymme.. (context) - Jessup - 1993
3   Computing accurate eigensytems of scaled diagonally dominant.. (context) - Barlow, Demmel - 1990
3   Exploiting fast matrix multiplication within the level 3 BLA.. (context) - Higham - 1990
3   Solution of linear algebraic systems with rectangular matric.. (context) - Faddeev, Kublanovskaja et al. - 1968
2   The complete pivoting conjecture for Gaussian elimination is.. - Edelman - 1992
2   On rank-revealing factorisations (context) - Chandrasekaran, Ipsen - 1994
2   Efficient computation of the singular value decomposition wi.. - Gu, Demmel et al. - 1994
1   IEEE Computer Society (context) - Standard, Arithmetic et al. - 1987
1   A one-sided Jacobi algorithm for computing the singular valu.. (context) - de Rijk - 1989
1   Factoring symmetric indefinite matrices on high-performance .. (context) - Jones, Patrick - 1994
1   Du Croz (context) - Dongarra
1   Computing eigenspaces with specified eigenvalues of a regula.. (context) - Kagstrom, Poromaa - 1994
1   Convergence of the shifted QR algorithm on 3 \Theta 3 normal.. (context) - Batterson - 1990

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