其他书籍

以下是关于矩阵计算和相关领域的一些专著,此类专著正在不断推陈出新. 从这些文献可以看到矩阵计算领域的历史发展脉络和所涉猎的广度.更专业的文 献在各节末尾的“注释与参考文献”中给出.

早期的代表性著作

V.N. Faddeeva (1959). Computational Methods of Linear Algebra, Dover, New York.

E. Bodewig (1959). Matrix Calculus, North-Holland, Amsterdam.

J.H. Wilkinson (1963). Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, NJ.

A.S. Householder (1964). Theory of Matrices in Numerical Analysis,Blaisdell, New York. Reprinted in 1974 by Dover, New York.

L. Fox (1964). An Introduction to Numerical Linear Algebra, Oxford University Press, Oxford.

J.H. Wilkinson (1965). The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.

矩阵计算的一般性著作

G.W. Stewart (1973). Introduction to Matrix Computations, Academic Press, New York.

R.J. Goult, R.F. Hoskins, J.A. Milner, and M.J. Pratt (1974). Computational Methods in Linear Algebra, John Wiley and Sons, New York.

W.W. Hager (1988). Applied Numerical Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ.

P.G. Ciarlet (1989). Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press, Cambridge.

P.E. Gill, W. Murray, and M.H. Wright (1991). Numerical Linear Algebra and Optimization, Vol. 1, Addison-Wesley, Reading, MA.

A. Jennings and J.J. McKeowen (1992). Matrix Computation, second edition, John Wileyand Sons, New York.

L.N. Trefethen and D. Bau III (1997). Numerical Linear Algebra, SIAM Publications,Philadelphia, PA.

J.W. Demmel (1997). Applied Numerical Linear Algebra, SIAM Publications, Philadelphia,PA.

A.J. Laub (2005). Matrix Analysis for Scientists and Engineers, SIAM Publications, Philadelphia, PA.

B.N. Datta (2010). Numerical Linear Algebra and Applications, second edition, SIAM Publications, Philadelphia, PA.

D.S. Watkins (2010). Fundamentals of Matrix Computations, John Wiley and Sons, New York.

A.J. Laub (2012). Computational Matrix Analysis, SIAM Publications, Philadelphia, PA.

B.N. Datta (2010). Numerical Linear Algebra and Applications, second edition, SIAM Publications,Philadelphia, PA.

D.S. Watkins (2010). Fundamentals of Matrix Computations, John Wiley and Sons, New York.

A.J. Laub (2012). Computational Matrix Analysis, SIAM Publications, Philadelphia, PA.

线性方程和最小二乘问题

G.E. Forsythe and C.B. Moler (1967). Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, NJ.

A. George and J.W-H. Liu (1981). Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs, NJ.

I.S. Duff, A.M. Erisman, and J.K. Reid (1986). Direct Methods for Sparse Matrices, Oxford University Press, New York.

R.W. Farebrother (1987). Linear Least Squares Computations, Marcel Dekker, New York.

C.L. Lawson and R.J. Hanson (1995). Solving Least Squares Problems, SIAM Publications,Philadelphia, PA.

Å. Björck (1996). Numerical Methods for Least Squares Problems, SIAM Publications,Philadelphia, PA.

G.W. Stewart (1998). Matrix Algorithms: Basic Decompositions, SIAM Publications,Philadelphia, PA.

N.J. Higham (2002). Accuracy and Stability of Numerical Algorithms, second edition, SIAM Publications, Philadelphia, PA.

T.A. Davis (2006). Direct Methods for Sparse Linear Systems, SIAM Publications, Philadelphia,PA.

I.C.F. Ipsen (2009). Numerical Matrix Analysis: Linear Systems and Least Squares, SIAM Publications, Philadelphia, PA.

特征值问题

A.R. Gourlay and G.A. Watson (1973). Computational Methods for Matrix Eigenproblems,John Wiley & Sons, New York.

F. Chatelin (1993). Eigenvalues of Matrices, John Wiley & Sons, New York.

B.N. Parlett (1998). The Symmetric Eigenvalue Problem, SIAM Publications, Philadelphia,PA.

G.W. Stewart (2001). Matrix Algorithms Volume II: Eigensystems, SIAM Publications,Philadelphia, PA.

L. Komzsik (2003). The Lanczos Method: Evolution and Application, SIAM Publications,Philadelphia, PA.

D. Kressner (2005). Numerical Methods for General and Structured Eigenvalue Problems,Springer, Berlin.

D.S. Watkins (2007). The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods,SIAM Publications, Philadelphia, PA.

Y. Saad (2011). Numerical Methods for Large Eigenvalue Problems, revised edition, SIAM Publications, Philadelphia, PA.

迭代方法

R.S. Varga (1962). Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ.

D.M. Young (1971). Iterative Solution of Large Linear Systems, Academic Press, New York.

L.A. Hageman and D.M. Young (1981). Applied Iterative Methods, Academic Press, New York.

J. Cullum and R.A. Willoughby (1985). Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. I Theory, Birkhaüser, Boston.

J. Cullum and R.A. Willoughby (1985). Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. II Programs, Birkhaüser, Boston.

W. Hackbusch (1994). Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, New York.

O. Axelsson (1994). Iterative Solution Methods, Cambridge University Press.

A. Greenbaum (1997). Iterative Methods for Solving Linear Systems, SIAM Publications,Philadelphia, PA.

Y. Saad (2003). Iterative Methods for Sparse Linear Systems, second edition, SIAM Publications,Philadelphia, PA.

H. van der Vorst (2003). Iterative Krylov Methods for Large Linear Systems, Cambridge University Press, Cambridge, UK.

G. Meurant (2006). The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations, SIAM Publications, Philadelphia, PA.

专题

L.N. Trefethen and M. Embree (2005). Spectra and Pseudospectra—The Behavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton and Oxford.

R. Vandebril, M. Van Barel, and N. Mastronardi (2007). Matrix Computations and Semiseparable Matrices I: Linear Systems, Johns Hopkins University Press, Baltimore, MD.

R. Vandebril, M. Van Barel, and N. Mastronardi (2008). Matrix Computations and Semiseparable Matrices II: Eigenvalue and Singular Value Methods, Johns Hopkins University Press, Baltimore, MD.

N.J. Higham (2008) Functions of Matrices, SIAM Publications, Philadelphia, PA.

文集

R.H. Chan, C. Greif, and D.P. O’Leary, eds. (2007). Milestones in Matrix Computation: Selected Works of G.H. Golub, with Commentaries, Oxford University Press, Oxford.

M.E. Kilmer and D.P. O’Leary, eds. (2010). Selected Works of G.W. Stewart, Birkhauser,Boston, MA.

算法实现

B.T. Smith, J.M. Boyle, Y. Ikebe, V.C. Klema, and C.B. Moler (1970). Matrix Eigensystem Routines: EISPACK Guide, second edition, Lecture Notes in Computer Science, Vol. 6,Springer-Verlag, New York.

J.H. Wilkinson and C. Reinsch, eds. (1971). Handbook for Automatic Computation, Vol. 2,Linear Algebra, Springer-Verlag, New York.

B.S. Garbow, J.M. Boyle, J.J. Dongarra, and C.B. Moler (1972). Matrix Eigensystem Routines: EISPACK Guide Extension, Lecture Notes in Computer Science, Vol. 51,Springer-Verlag, New York.

J.J. Dongarra, J.R. Bunch, C.B. Moler, and G.W. Stewart (1979). LINPACK Users’ Guide,SIAM Publications, Philadelphia, PA.

K. Gallivan, M. Heath, E. Ng, B. Peyton, R. Plemmons, J. Ortega, C. Romine, A. Sameh,and R. Voigt (1990). Parallel Algorithms for Matrix Computations, SIAM Publications,Philadelphia, PA.

R. Barrett, M.W. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R.Pozo, C. Romine, and H. van der Vorst (1993). Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM Publications, Philadelphia, PA.

L.S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S.Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R.C. Whaley (1997).ScaLAPACK Users’ Guide, SIAM Publications, Philadelphia, PA.

J.J. Dongarra, I.S. Duff, D.C. Sorensen, and H.A. van der Vorst (1998). Numerical Linear Algebra on High-Performance Computers, SIAM Publications, Philadelphia, PA.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A.Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen (1999). LAPACK Users’Guide, third edition, SIAM Publications, Philadelphia, PA.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (2000). Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM Publications,Philadelphia, PA.

V.A. Barker, L.S. Blackford, J. Dongarra, J. Du Croz, S. Hammarling, M. Marinova, J.Wasniewski, and P. Yalamov (2001). LAPACK95 Users’ Guide, SIAM Publications,Philadelphia.

MATLAB 软件

D.J. Higham and N.J. Higham (2005). MATLAB Guide, second edition, SIAM Publications, Philadelphia, PA.

R. Pratap (2006). Getting Started with Matlab 7, Oxford University Press, New York.

C.F. Van Loan and D. Fan (2009). Insight Through Computing: A Matlab Introduction toComputational Science and Engineering, SIAM Publications, Philadelphia, PA.

矩阵代数与分析

R. Horn and C. Johnson (1985). Matrix Analysis, Cambridge University Press, New York.

G.W. Stewart and J. Sun (1990). Matrix Perturbation Theory, Academic Press, San Diego.

R. Horn and C. Johnson (1991). Topics in Matrix Analysis, Cambridge University Press,New York.

D.S. Bernstein (2005). Matrix Mathematics, Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.

L. Hogben (2006). Handbook of Linear Algebra, Chapman and Hall, Boca Raton, FL.

科学计算/数值分析

G.W. Stewart (1996). Afternotes on Numerical Analysis, SIAM Publications, Philadelphia,PA.

C.F. Van Loan (1997). Introduction to Scientific Computing: A Matrix-Vector Approach Using Matlab, Prentice Hall, Upper Saddle River, NJ.

G.W. Stewart (1998). Afternotes on Numerical Analysis: Afternotes Goes to Graduate School, SIAM Publications, Philadelphia, PA.

M.T. Heath (2002). Scientific Computing: An Introductory Survey, second edition, McGraw-Hill, New York.

C.B. Moler (2008) Numerical Computing with MATLAB, revised reprint, SIAM Publications,Philadelphia, PA.

G. Dahlquist and Å. Björck (2008). Numerical Methods in Scientific Computing, Vol. 1,SIAM Publications, Philadelphia, PA.

U. Ascher and C. Greif (2011). A First Course in Numerical Methods, SIAM Publications,Philadelphia, PA.

目录