AMSC/CMSC 666 Texts and Other Resourses
Spring 2005

Required Text

• Josef Stoer and Roland Bulirsch,
  Introduction to Numerical Analysis, Third Edition
  Texts in Applied Mathematics 12,
  Springer-Verlag, New York, 2002
  Roughly, we will cover Chapters 2, 3, 6, and 8.
  It will be expected that you know some of Chapters 1 and 4.

Notes

• Vector and Matrix Norms

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MATLAB Resourses

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Related General Texts

• A.K. Atkinson, An Introduction to Numerical Analysis, Wiley, 1978.
• E. Isaacson and H.B. Keller, Analysis of Numerical Methods, Dover, 1994.

Approximation Theory and Methods

• E.W. Cheney, Introduction to Approximation Theory, McGraw-Hill, New York, 1966.
• P.J. Davis, Interpolation and Approximation, Dover, 1975.
• P.J. Davis and P.H. Rabinowitz, Methods of Numerical Integration, Academic Press, 1975.
• C. de Boor, A Practical Guide to Splines, Springer-Verlag, 1978.
• G. Lorentz, Approximation of Functions, Holt, Rinehart, and Winston, 1966.
• H. Engles, Numerical Quadrature and Cubature, Academic Press, 1980.
• P.M.J.D. Powell, Approximation Theory and Methods, Cambridge University Press, 1981.
• T. J. Rivlin, Introduction to the Approximation of Functions, Dover, 1987.
• L.L. Schumaker, Spline Functions: Basic Theory, revised ed., Krieger Publishing Company, 1993.
• A. Stroud, Approximate Calculation of Multiple Integrals, Prentice-Hall, 1971.
• G. Szgo, Orthogonal Polynomials, 3rd ed., Amer. Math. Soc., 1967.

Numerical Linear Algebra

• O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1994.
• G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, 1996.
• W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, 1994.
• L.A. Hageman and D.M. Young, Applied Iterative Methods, Academic Press, 1981.
• A.S. Householder, Theory of Matrices in Numerical Analysis, Blaisdell, 1964, Dover, 1974.
• B.N. Parlett, The Symmetric Eigenvalue Problem, Prentice Hall, 1980.
• Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, 1996.
• Y. Saad, Numerical Methods for Large Eigenvalue Problems: Theory and Algorithms, John Wiley & Sons, 1992.
• G.W. Stewart, Introduction to Matrix Computations, Academic Press, 1973.
• L.N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM, 1997.
• R.S. Varga, Matrix Iterative Analysis, 2nd ed., Springer Series in Computational Mathematics 27 , Springer-Verlag, New York, 2000.
• J.H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, 1965.
• D.M. Young, Iterative Solution of Large Linear Systems, Academic Press, 1971.

Nonlinear Equations and Numerical Optimization

• J.E. Dennis Jr. and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, 1983, SIAM, 1996.
• R. Fletcher, Practical Methods of Optimization, Vol. 1: Unconstrained Optimization, Wiley, 1980.
• R. Fletcher, Practical Methods of Optimization, Vol. 2: Constrained Optimization, Wiley, 1981.
• P.E. Gill, W. Murray, and M.H. Wright, Practical Optimization, Academic Press, 1981.
• D. Luenberger, Linear and Nonlinear Programming, Wiley, 1984.
• J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, 1970.
• W.C. Rheinboldt, Methods for Solving Systems of Nonlinear Equations, CBMS-NSF Regional Conference Series in Applied Mathematics 70 , 2nd ed., SIAM, 1998.

Numerical Solution of Ordinary Differential Equations

• J. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, 1987.
• J.D. Lambert, Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, John Wiley & Son, 1991.
• L.F. Shampine, Numerical Solution of Ordinary Differential Equations, CRC Press, 1994.
• H. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations, Springer-Verlag, 1973.

Numerical Solution of Partial Differential Equations

• O. Axelsson and V.A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic Press, London, 1984.
• S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, 1996.
• F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics 15 , Springer-Verlag, New York, 1991.
• W.L. Briggs, V.E. Henson, and S.F. McCormick, A Multigrid Tutorial, SIAM, 2000.
• P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, 1978.
• P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part I), North-Holland, 1991.
• G.E. Forsythe and W.R. Wasow, Finite-Difference Methods for Partial Differential Equations, Wiley, 1960.
• D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 26 , SIAM, 1977.
• B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods, Wiley, 1995.
• T.J.R. Hughes, The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1987, Dover, 2000.
• C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, 1987.
• R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd ed., Birkhauser Verlag, 1992.
• A.R. Mitchell and R. Wait, The Finite Element Method in Partial Differential Equations, John Wiley & Sons, Ltd, 1977.
• K.W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 1995.
• R.D. Richtmyer and K.W. Morton, Difference Methods for Initial-value Problems, 2nd ed., Interscience, Wiley, 1967.
• H.R. Schwarz, Finite Element Methods in Computational Mathematics and Applications, Academic Press, 1988.
• G.D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Oxford University Press, 1986.
• W.G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Wellesley Cambridge Press, 1973.
• J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, 1989.
• P. Wesseling, An Introduction to Multigrid Methods, Wiley, 1992.
• O.C. Zienkiewicz and K. Morgan, Finite Elements and Approximation, John Wiley & Sons, 1983.
• O.C. Zienkiewicz, The Finite Element Method, 3rd ed., McGraw-Hill, New York, 1977.