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Numerical analysis and scientific computing (book list)

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This is a section of the Basic Math Library List


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16. Numerical analysis and scientific computing
    Design of numerical algorithms and analysis of their accuracy, stability and complexity. 
    Approximation theory. Applied and computational aspects of harmonic analysis. 
    Numerical solution of algebraic, functional, differential, and integral equations. 
    Grid generation and adaptivity.
    Connections with sections  8, 10, 11, 13, 15, 17, 18.


Numerical Analysis: Introductory Texts

  • Atkinson, Kendall E. Elementary Numerical Analysis New York, NY: John Wiley, 1978, 1985.
      • Burden, Richard L. and Faires, J. Douglas. Numerical Analysis, Boston, MA: PWS-Kent, 1989. Fourth Edition.

Cheney, Elliot W. and Kincaid, David R. Numerical Mathematics and Computing, Pacific Grove, CA: Brooks/Cole, 1980, 1985. Second Edition.

  • Conte, Samuel D. and de Boor, Carl. Elementary Numerical Analysis: An Algorithmic Approach, New York, NY: McGraw-Hill, 1972, 1980. Third Edition.
    • Davis, Philip F. and Rabinowitz, Philip. Methods of Numerical Integration, New York, NY: Academic Press, 1975, 1984. Second Edition.

Dorn, William S. and McCracken, Daniel D. Numerical Methods with FORTRAN IV Case Studies New York, NY: John Wiley, 1972.

  • Gerald, Curtis F. and Wheatley, Patrick O. Applied Numerical Analysis, Reading, MA: Addison-Wesley, 1978, 1989. Fourth Edition.
  • Hamming, Richard W. Introduction to Applied Numerical Analysis New York, NY: Hemisphere, 1989.

Johnson, Lee W. and Riess, R. Dean. Numerical Analysis, Reading, MA: Addison-Wesley, 1977, 1982. Second Edition.

      • Kincaid, David R. and Cheney, Elliot W. Numerical Analysis: Mathematics of Scientific Computing Pacific Grove, CA: Brooks/Cole, 1991.

Maron, Melvin J. and Lopez, Robert J. Numerical Analysis: A Practical Approach, Belmont, CA: Wadsworth, 1991. Third Edition.

  • Mathews, John H. Numerical Methods for Computer Science, Engineering, and Mathematics Englewood Cliffs, NJ: Prentice Hall, 1987.

Morris, J. Ll. Computational Methods in Elementary Numerical Analysis New York, NY: John Wiley, 1983.

Ralston, Anthony and Rabinowitz, Philip. A First Course in Numerical Analysis, New York, NY: McGraw-Hill, 1978. Second Edition.

    • Stoer, J. and Bulirsch, R. Introduction to Numerical Analysis New York, NY: Springer-Verlag, 1980.

Numerical Analysis: Advanced Surveys

  • Carnahan, Brice; Luther, H.A.; and Wilkes, James O. Applied Numerical Methods New York, NY: John Wiley, 1969.

Churchhouse, Robert F., ed. Numerical Methods New York, NY: John Wiley, 1981. Handbook of Applicable Mathematics, Volume III.

Dahlquist, Germund and Ake Bjorck. Numerical Methods Englewood Cliffs, NJ: Prentice Hall, 1974.

    • Golub, Gene H., ed. Studies in Numerical Analysis Washington, DC: Mathematical Association of America, 1984.
    • Greenspan, Donald and Casulli, Vincenzo. Numerical Analysis for Applied Mathematics, Science, and Engineering Reading, MA: Addison-Wesley, 1988.

Jacques, Ian and Judd, Colin. Numerical Analysis New York, NY: Chapman and Hall, 1987.

Jain, M.K.; Iyengar, S.R.K.; and Jain, R.K. Numerical Methods for Scientific and Engineering Computation New York, NY: Halsted Press, 1985.

  • Ortega, James M. Numerical Analysis: A Second Course Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990.

Todd, John. Basic Numerical Mathematics, New York, NY: Birkhauser, 1977, 1979. 2 Vols.

Traub, Joseph F. Iterative Methods for the Solution of Equations New York, NY: Chelsea, 1982.

Vandergraft, James S. Introduction to Numerical Computations New York, NY: Academic Press, 1978.

Young, David M. and Gregory, Robert T. A Survey of Numerical Mathematics, Reading, MA: Addison-Wesley, 1972, 1973. 2 Vols.

Numerical Analysis: Differential Equations

Axelsson, O. and Barker, V.A. Finite Element Solution of Boundary Value Problems: Theory and Computation New York, NY: Academic Press, 1984.

  • Bathe, Klaus-Jurgen and Wilson, Edward L. Numerical Methods in Finite Element Analysis Englewood Cliffs, NJ: Prentice Hall, 1976.

Ciarlet, Philippe G. The Finite Element Method for Elliptic Problems Amsterdam: North-Holland, 1978.

Hall, G. and Watt, J.M., eds. Modern Numerical Methods for Ordinary Differential Equations New York, NY: Clarendon Press, 1976.

Henrici, Peter. Discrete Variable Methods in Ordinary Differential Equations New York, NY: John Wiley, 1962.

Jain, M.K. Numerical Solution of Differential Equations New York, NY: Halsted Press, 1979.

  • Keller, H.B. Numerical Methods for Two-Point Boundary-Value Problems New York, NY: John Wiley, 1968.
  • Lapidus, Leon and Pinder, George F. Numerical Solution of Partial Differential Equations in Science and Engineering New York, NY: John Wiley, 1982.

Meis, Theodor and Marcowitz, Ulrich. Numerical Solution of Partial Differential Equations New York, NY: Springer-Verlag, 1981.

Parker, Thomas S. and Chua, Leon O. Practical Numerical Algorithms for Chaotic Systems New York, NY: Springer-Verlag, 1989.

  • Quinney, Douglas. An Introduction to the Numerical Solution of Differential Equations New York, NY: John Wiley, 1985.
  • Sewell, Granville. The Numerical Solution of Ordinary and Partial Differential Equations New York, NY: Academic Press, 1988.
  • Smith, G.D. Numerical Solution of Partial Differential Equations: Finite Difference Methods, New York, NY: Clarendon Press, 1978, 1985. Third Edition.
  • Sod, Gary A. Numerical Methods in Fluid Dynamics: Initial and Initial Boundary-Value Problems New York, NY: Cambridge University Press, 1985.

Twizell, E.H. Computational Methods for Partial Differential Equations New York, NY: Halsted Press, 1984.

Vemuri, V. and Karplus, Walter J. Digital Computer Treatment of Partial Differential Equations Englewood Cliffs, NJ: Prentice Hall, 1981.

Numerical Linear Algebra

    • Ciarlet, Philippe G. Numerical Linear Algebra New York, NY: Cambridge University Press, 1989.
    • Coleman, Thomas F. and Van Loan, Charles F. Handbook for Matrix Computations Philadelphia, PA: Society for Industrial and Applied Mathematics, 1988.

Forsythe, George E. and Moler, Cleve B. Computer Solution of Linear Algebraic Systems Englewood Cliffs, NJ: Prentice Hall, 1967.

      • Golub, Gene H. and Van Loan, Charles F. Matrix Computations, Baltimore, MD: Johns Hopkins University Press, 1983, 1989. Second Edition.

Hager, William. Applied Numerical Linear Algebra Englewood Cliffs, NJ: Prentice Hall, 1988.

  • Hill, David R. and Moler, Cleve B. Experiments in Computational Matrix Algebra Cambridge, MA: Random House, 1987.

Jennings, Alan. Matrix Computation for Engineers and Scientists New York, NY: John Wiley, 1977.

  • Magid, Andy R. Applied Matrix Models: A Second Course in Linear Algebra with Computer Applications New York, NY: John Wiley, 1985.

Pissanetzky, Sergio. Sparse Matrix Technology New York, NY: Academic Press, 1984.

  • Rice, John R. Matrix Computations and Mathematical Software New York, NY: McGraw-Hill, 1981.

Stewart, G.W. Introduction to Matrix Computation New York, NY: Academic Press, 1973.

Varga, Richard S. Matrix Iterative Analysis Englewood Cliffs, NJ: Prentice Hall, 1962.

      • Wilkinson, James H. The Algebraic Eigenvalue Problem New York, NY: Oxford University Press, 1965, 1988.

Young, David M. Iterative Solution of Large Linear Systems New York, NY: Academic Press, 1971.


Approximation Theory

      • Cheney, Elliot W. Introduction to Approximation Theory, New York, NY: Chelsea, 1966, 1982. Second Edition.
    • Davis, Philip J. Interpolation and Approximation Mineola, NY: Dover, 1975.

Feinerman, Robert P. and Newman, Donald J. Polynomial Approximation Baltimore, MD: Williams and Wilkins, 1974.

Hestenes, Magnus R. Conjugate Direction Methods in Optimization New York, NY: Springer-Verlag, 1980.

  • Lorentz, G.G. Approximation of Functions, New York, NY: Chelsea, 1986. Second Edition.

Prenter, P.M. Splines and Variational Methods New York, NY: John Wiley, 1975.

Rivlin, Theodore J. An Introduction to the Approximation of Functions Mineola, NY: Dover, 1981.

  • Wahba, Grace. Spline Models for Observational Data Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990.
  • Watson, G.A. Approximation Theory and Numerical Methods New York, NY: John Wiley, 1980.
    • de Boor, Carl. A Practical Guide to Splines New York, NY: Springer-Verlag, 1978.

de Bruijn, N.G. Asymptotic Methods in Analysis Mineola, NY: Dover, 1981.


Numerical Analysis: Computer Methods

  • Forsythe, George E.; Malcolm, Michael A.; and Moler, Cleve B. Computer Methods for Mathematical Computations Englewood Cliffs, NJ: Prentice Hall, 1977.
  • Froberg, Carl-Erik. Numerical Mathematics: Theory and Computer Applications Redwood City, CA: Benjamin Cummings, 1985.
    • Grandine, Thomas A. The Numerical Methods Programming Projects Book New York, NY: Oxford University Press, 1990.
  • James, M.L.; Smith, G.M.; and Wolford, J.C. Applied Numerical Methods for Digital Computation, New York, NY: Harper and Row, 1985. Third Edition.

Johnston, R.L. Numerical Methods: A Software Approach New York, NY: John Wiley, 1982.

Kahaner, David; Moler, Cleve B.; and Nash, Stephen. Numerical Methods and Software Englewood Cliffs, NJ: Prentice Hall, 1989.

Kopchenova, N.V. and Maron, I.A. Computational Mathematics: Worked Examples and Problems with Elements of Theory Moscow: MIR, 1981.

Lastman, Gary J. and Sinha, Naresh K. Microcomputer-Based Numerical Methods for Science and Engineering New York, NY: W.B. Saunders, 1989.

  • Mohamed, J.L. and Walsh, J.E., eds. Numerical Algorithms New York, NY: Clarendon Press, 1986.
      • Press, William H., et al. Numerical Recipes: The Art of Scientific Computing New York, NY: Cambridge University Press, 1986.

Schendel, U. Introduction to Numerical Methods for Parallel Computers New York, NY: Halsted Press, 1984.


Numerical Analysis: Special Topics

Baker, Christopher T.H. The Numerical Treatment of Integral Equations New York, NY: Clarendon Press, 1977.

Brigham, E. Oran. The Fast Fourier Transform Englewood Cliffs, NJ: Prentice Hall, 1974.

  • Delves, L.M. and Mohamed, J.L. Computational Methods for Integral Equations New York, NY: Cambridge University Press, 1985.

Irons, Bruce and Shrive, Nigel G. Finite Element Primer New York, NY: Halsted Press, 1983.

Zienkiewicz, O.C. The Finite Element Method New York, NY: McGraw-Hill, 1977.

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