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Theory of real computation according to egc
 Reliable Implementation of Real Number Algorithms: Theory and Practice, volume 5045 of Lecture Notes in Computer Science
, 2008
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Accurate and efficient expression evaluation and linear algebra
, 2008
"... We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correc ..."
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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate ’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the socalled traditional model (TM), where the computed result of op(a, b), a binary operation like a + b, is given by op(a, b) ∗ (1 + δ) where all we know is that δ  ≤ε ≪ 1. Here ε is a constant also known as machine epsilon.
Tropical Algebraic Geometry in Maple  a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients
, 2009
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Solving the principal minor assignment problem and related computations
, 2006
"... find it satisfactory and recommend that it be accepted. Chair ii ACKNOWLEDGMENTS I would like to express my deep gratitude to my advisor Dr. Michael J. Tsatsomeros for his consistent guidance, unwavering encouragement and especially for his gift for asking the right questions. I have recognized him ..."
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find it satisfactory and recommend that it be accepted. Chair ii ACKNOWLEDGMENTS I would like to express my deep gratitude to my advisor Dr. Michael J. Tsatsomeros for his consistent guidance, unwavering encouragement and especially for his gift for asking the right questions. I have recognized him as a truly great teacher from my first semester at Washington State. I would also like to thank the other members of my committee, Dr. David Watkins and Dr. Haijun Li, for their help and support. I will always be grateful to the staff and the professors at WSU for making my experience here so educational and valuable. I express appreciation to an anonymous referee for a careful examination of the first draft of [13] leading to the introduction of condition (c) of Definition 3.2.3 and for several other improvements that have been incorporated into this dissertation. Finally, I would like to acknowledge the faithful support of a loving family that has given me the power to accomplish all that I have in life. Special credit goes to my parents Don and Marilyn, my wife Liz, and my children Joshua, Maeve and Jacob. iii