Secondary References for MCS 563
Although we follow "Numerical Polynomial Algebra" closely,
we cannot resist listing several secondary references,
organized according to the most related chapter in our textbook.
Chapter 1
-
"Computer Algebra Handbook.
Foundations, Applications, Systems."
Edited by Johannes Grabmeier, Erich Kaltofen,
and Volker Weispfennig, Springer 2003.
Look for the relation between computer algebra
and scientific computing.
Chapter 2
- David Cox, John Little, and Donal O'Shea:
"Ideals, Varieties, and Algorithms.
An introduction to Computational Algebraic Geometry
and Commutative Algebra". Second Edition, Springer 1997.
Offers a nice introduction to the algebro-geometric dictionary,
Chapter 3
-
Leonore Blum, Felipe Cucker, Michael Shub, and Steve Smale:
"Complexity and Real Computation". Springer, 1998.
Introduces a continuous model of computation and an alpha-theory
to certify zeros.
Chapter 4
-
Nicholas J. Higham: "Accuracy and Stability of Numerical Algorithms"
SIAM 1996.
Lists principles of finite precision computation and much more.
Chapter 5
-
Dario Bini and Victor Pan: "Polynomial and Matrix Computations"
Birkhauser, 1994.
Chapter 6
An invitation to apply recent research results to a problem
from image processing:
- Zhonggang Zeng: "Computing multiple roots of inexact polynomials"
Math. Comp. electronically posted on July 22, 2004.
- Zhonggang Zeng: Algorithm 835: MultRoot -- A Matlab package computing
polynomial roots and multiplicities", ACM Transaction on Mathematical
Software, Volume 30, pages 218-315, 2004.
- S. Unnikrishna Pillai and Ben Liang: "Blind Image Deconvolution Using
a Robust GCD Approach", IEEE Transactions on Image Processing,
Volume 8, Number 2, pages 295-301, 1999.
Chapter 7
- Andreas Griewank: "Evaluating derivatives: principles and techniques
of algorithmic differentiation"
Chapter 8
-
Bernd Sturmfels: "Solving Systems of Polynomial Equations"
CMBS Regional Conference Series in Mathematics, Number 97,
AMS 2002.