Introduction to Numerical Analysis I

AMSC 466, Fall 2026


Course Information

LectureJMP 1109 TuTh 11-12:15pm
InstructorProfessor Eitan Tadmor
Contacttel: x5-0648   email:
Office HoursBy appointment 4141 CSIC Bldg. #406
Grader
Midterm
Final
Grading10% Homework, 40% Mid-Term, 50% Final


Course Description

  1. DIRECT METHODS for Solving Systems of Linear Equations

    1. Introduction: Cramer's rule; triangular and unitary systems
    2. Gauss elimination: multipliers, operation count
    3. LU decompositions: symmetric, positive definite, banded, Hessenberg,...
    4. Pivoting

      5. Assignment #1
    5. Backward error analysis: ill-conditioning, condition number, backward error estimates

    6. QR decompositions: Householder reflections, stability, least-squares

      7. Assignment #2
    7. Beyond LU and QR decompositions:

      8. Assignment #3

  2. INTERPOLATION

    1. Lagrange and Newton interpolants
      2. Assignment #4
    2. Interpolation with derivatives
      3. Assignment #5
    3. Interplolation of data in equi-spaced nodes
      4. Assignment #6
      MID-TERM

  3. LEAST-SQUARES PROBLEMS

    1. Normal equations
    2. Orthogonal polynomials: Legendre, Chebyshev, ...
      3. Assignment #7

  4. NUMERICAL DIFFERETIATION; NUMERICAL INTEGRATION

    1. Numerical differentiation
      Assignment #8
    2. Gauss quadrature rules
    3. Newton-Cotes rules -- numerical integration with equi-spaced nodes
    4. Composite quadrature rules -- trapezoidal, Simpson, ...
      5. Assignment #9

  5. ITERATIVE METHODS for Solution of Nonlinear Equations

    1. Fixed point iterations
    2. Scalar equations
    3. Systems of equations
      4. Assignment #10

    References

    Recommended reference book

    GENERAL TEXTBOOKS

    K. Atkinson, An INTRODUCTION to NUMERICAL ANALYSIS, Wiley, 1987

    S. Conte & C. deBoor, ELEMENTARY NUMERICAL ANALYSIS, McGraw-Hill
    User friendly; Shows how 'it' works; Proofs, exercises and notes

    G. Dahlquist & A. Bjorck, NUMERICAL METHODS, Prentice-Hall,
    User friendly; Shows how 'it' works; Exercises

    E. Isaacson & H. Keller, ANALYSIS of NUMERICAL METHODS, Wiley
    The 'First'; Proofs; out-dated in certain aspects; Encrypted message in Preface

    A. Ralston & P. Rabinowitz, FIRST COURSE in NUMERICAL ANALYSIS, 2nd ed., McGraw-hill,
    Detailed; Scholarly written; Comprehensive; Proofs exercises and notes

    J. Stoer & R. Bulrisch, INTRODUCTION TO NUMERICAL ANALYSIS, 2nd ed., Springer
    detailed account on approximation, linear solvers & eigen-solvers, ODE solvers,..

    B. Wendroff, THEORETICAL NUMERICAL ANALYSIS, Academic Press, 1966
    Only the 'Proofs'; elegant presentation

    APPROXIMATION THEORY

    E. W. Cheney, INTRODUCTION TO APPROXIMATION THEORY
    Classical

    P. Davis, INTERPOLATION & APPROXIMATION, Dover
    Very readable

    T. Rivlin, AN INTRODUCTION to the APPROXIMATION of FUNCTIONS
    Classical

    R. DeVore & G. Lorentz, CONSTRUCTIVE APPROXIMATION, Springer
    A detailed account from classical theory to the modern theory; everything; Proofs exercises and notes

    NUMERICAL INTEGRATION

    F. Davis & P. Rabinowitz, NUMERICAL INTEGRATION,
    Everything...

    Eitan Tadmor