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Correctness Proofs Outline for NewtonRaphson Based FloatingPoint Divide and Square Root Algorithms
"... This paper describes a study of a class of algorithms for the floatingpoint divide and square root operations, based on the NewtonRaphson iterative method. The two main goals were: (1) Proving the IEEE correctness of these iterative floatingpoint algorithms, i.e. compliance with the IEEE754 sta ..."
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Cited by 23 (0 self)
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This paper describes a study of a class of algorithms for the floatingpoint divide and square root operations, based on the NewtonRaphson iterative method. The two main goals were: (1) Proving the IEEE correctness of these iterative floatingpoint algorithms, i.e. compliance with the IEEE754
Decimal FloatingPoint Square Root Using NewtonRaphson Iteration
 Proc. 16th IEEE Int’l Conf. ApplicationSpecific Systems, Architectures and Processors (ASAP ’05
, 2005
"... With continued reductions in feature size, additional functionality may be added to future microprocessors to boost the performance of important application domains. Due to growth in commercial, financial, and Internetbased applications, decimal floating point arithmetic is now attracting more atte ..."
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Cited by 4 (0 self)
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Arithmetic (IEEE754R). This paper presents an efficient arithmetic algorithm and hardware design for decimal floatingpoint square root. This design uses an optimized piecewise linear approximation, a modified NewtonRaphson iteration, a specialized rounding technique, and a modified decimal multiplier
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 707 (18 self)
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The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new
Proving the IEEE Correctness of Iterative FloatingPoint Square Root, Divide, and Remainder Algorithms
"... The work presented in this paper was initiated as part of a study on software alternatives to the hardware implementations of floatingpoint operations such as divide and square root. The results of the study proved the viability of software implementations, and showed that certain proposed algorith ..."
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Cited by 22 (2 self)
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algorithms are comparable in performance to current hardware implementations. This paper discusses two components of that study: (1) A methodology for proving the IEEE correctness of the result of iterative algorithms that implement the floatingpoint square root, divide, or remainder operation. (2
Area And Performance Tradeoffs In FloatingPoint Divide And Square Root Implementations
, 1994
"... ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, N ..."
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, NY 10036 USA, fax +1 (212) 8690481, or permissions@acm.org. AREA AND PERFORMANCE TRADEOFFS IN FLOATINGPOINT DIVIDE AND SQUARE ROOT IMPLEMENTATIONS Peter Soderquist Miriam Leeser School of Electrical Engineering Dept. of Electrical and Computer Engineering Cornell University Northeastern
Understanding convergence and stability of the NewtonRaphson method
"... Approximated solution of one and multivariable equations is an important part of numerical mathematics. The easiest case of the NewtonRaphson method leads to the xn+1 = xn − f(xn) f ′ formula which is both easy to prove and (xn) memorize, and it is also very effective in real life problems. However ..."
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Approximated solution of one and multivariable equations is an important part of numerical mathematics. The easiest case of the NewtonRaphson method leads to the xn+1 = xn − f(xn) f ′ formula which is both easy to prove and (xn) memorize, and it is also very effective in real life problems
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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for additive expansions based on any tting criterion. Specic algorithms are presented for least{squares, least{absolute{deviation, and Huber{M loss functions for regression, and multi{class logistic likelihood for classication. Special enhancements are derived for the particular case where the individual
Results 1  10
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60,955