Polynomials
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IEEE Organizations related to Polynomials
Back to TopConferences related to Polynomials
Back to Top2014 IEEE International Symposium on Information Theory (ISIT)
Annual international symposium on processing, transmission, storage, and use of information, as well as theoretical and applied aspects of coding, communications, and communications networks.
2010 15th Conference on Microwave Techniques (COMITE 2010)
Microwave techniques, antennas, optoelectronics, computational electromagnetics.
2010 IEEE 51st Annual Symposium on Foundations of Computer Science (FOCS)
The 51st Annual Symposium on Foundations of Computer Science (FOCS2010), sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing, will be held at the Monte Carlo Hotel in Las Vegas, Nevada, October 2426, 2010. A series of tutorial presentations will be given on October 23. Papers presenting new and original research on the theory of computation are sought, including papers that broaden the reach of computer science theory, or raise important problems that can ben
2009 ISECS International Colloquium on Computing, Communication, Control, and Management (CCCM 2009)
Just like the name of the Colloquium, the theme for this conference is Advancing Computing, Communication, Control,and Management Technologies. Only original high quality papers related to this theme are especially solicited, including theories, methodologies, and applications in Computing, Communication, Control, and Management. Topics covering industrial issues/applications and academic research will be welcome.
Periodicals related to Polynomials
Back to TopCircuits and Systems I: Regular Papers, IEEE Transactions on
Part I will now contain regular papers focusing on all matters related to fundamental theory, applications, analog and digital signal processing. Part II will report on the latest significant results across all of these topic areas.
Computers, IEEE Transactions on
Design and analysis of algorithms, computer systems, and digital networks; methods for specifying, measuring, and modeling the performance of computers and computer systems; design of computer components, such as arithmetic units, data storage devices, and interface devices; design of reliable and testable digital devices and systems; computer networks and distributed computer systems; new computer organizations and architectures; applications of VLSI ...
Signal Processing, IEEE Transactions on
The technology of transmission, recording, reproduction, processing, and measurement of speech; other audiofrequency waves and other signals by digital, electronic, electrical, acoustic, mechanical, and optical means; the components and systems to accomplish these and related aims; and the environmental, psychological, and physiological factors of thesetechnologies.
Xplore Articles related to Polynomials
Back to TopInvariant Pattern Recognition Using Radial Tchebichef Moments
Bin Xiao; JianFeng Ma; JiangTao Cui 2010 Chinese Conference on Pattern Recognition (CCPR), 2010
Radial Tchebichef moments as a discrete orthogonal moment in the polar coordinate have been successfully used in the field of pattern recognition. However, the scaling invariant property of these moments has not been studied due to the complexity of the problem. In this paper, we present a new method to construct a complete set of scaling and rotation invariants extract ...
Complexity analysis and speedup techniques for optimal buffer insertion with minimum cost
Weiping Shi; Zhuo Li; C. J. Alpert ASPDAC 2004: Asia and South Pacific Design Automation Conference 2004 (IEEE Cat. No.04EX753), 2004
As gate delays d e e m faster than wire delays for each teehnolagy generation, buffer insertion hecomes a popular method to reduce the interconnecI delay. Several modem huffer insertion algorithms (e.g.. 17.6.151) are based on van Ginneken??s dynamic programming paradigm [141. However, van Ginneken??s original algorithm does not control buffering resources and tends to over buffering, thereby wasting area ...
Common information of random linear network coding over a 1hop broadcast packet erasure channel
ChihChun Wang; Jaemin Han 2011 IEEE International Symposium on Information Theory Proceedings, 2011
Random linear network coding (RLNC) is widely used in practical network coding (NC) protocol design. Recent results show that RLNC also plays an important role in capacityachieving intersession NC schemes for erasurebased 1hop relay networks. This work quantifies the common information of RLNC over a 1hop broadcast packet erasure channel. Several potential applications are discussed, including source coding, intersession NC, ...
A stability theorem for discrete systems
H. Schussler IEEE Transactions on Acoustics, Speech, and Signal Processing, 1976
A theorem is presented and proven, dealing with interesting properties of a polynomial D(z), being the denominator of the transfer function of a stable discrete system. The relationships to equivalent properties of a Hurwitz polynomial are considered.
E. N. Malamas; V. Paliouras; T. Stouraitis Proceedings of Third International Conference on Electronics, Circuits, and Systems, 1996
In this paper, algorithms and architectures for the evaluation of trigonometric functions in the Logarithmic Number System (LNS) are described. A novel algorithm for the computation of the LNS cosine, based on the subtraction function, is presented and extended to compute all trigonometric functions. The proposed algorithms show a major advantage over other methods in terms of memory requirements (up ...
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Educational Resources on Polynomials
Back to TopeLearning
Invariant Pattern Recognition Using Radial Tchebichef Moments
Bin Xiao; JianFeng Ma; JiangTao Cui 2010 Chinese Conference on Pattern Recognition (CCPR), 2010
Radial Tchebichef moments as a discrete orthogonal moment in the polar coordinate have been successfully used in the field of pattern recognition. However, the scaling invariant property of these moments has not been studied due to the complexity of the problem. In this paper, we present a new method to construct a complete set of scaling and rotation invariants extract ...
Complexity analysis and speedup techniques for optimal buffer insertion with minimum cost
Weiping Shi; Zhuo Li; C. J. Alpert ASPDAC 2004: Asia and South Pacific Design Automation Conference 2004 (IEEE Cat. No.04EX753), 2004
As gate delays d e e m faster than wire delays for each teehnolagy generation, buffer insertion hecomes a popular method to reduce the interconnecI delay. Several modem huffer insertion algorithms (e.g.. 17.6.151) are based on van Ginneken??s dynamic programming paradigm [141. However, van Ginneken??s original algorithm does not control buffering resources and tends to over buffering, thereby wasting area ...
Common information of random linear network coding over a 1hop broadcast packet erasure channel
ChihChun Wang; Jaemin Han 2011 IEEE International Symposium on Information Theory Proceedings, 2011
Random linear network coding (RLNC) is widely used in practical network coding (NC) protocol design. Recent results show that RLNC also plays an important role in capacityachieving intersession NC schemes for erasurebased 1hop relay networks. This work quantifies the common information of RLNC over a 1hop broadcast packet erasure channel. Several potential applications are discussed, including source coding, intersession NC, ...
A stability theorem for discrete systems
H. Schussler IEEE Transactions on Acoustics, Speech, and Signal Processing, 1976
A theorem is presented and proven, dealing with interesting properties of a polynomial D(z), being the denominator of the transfer function of a stable discrete system. The relationships to equivalent properties of a Hurwitz polynomial are considered.
E. N. Malamas; V. Paliouras; T. Stouraitis Proceedings of Third International Conference on Electronics, Circuits, and Systems, 1996
In this paper, algorithms and architectures for the evaluation of trigonometric functions in the Logarithmic Number System (LNS) are described. A novel algorithm for the computation of the LNS cosine, based on the subtraction function, is presented and extended to compute all trigonometric functions. The proposed algorithms show a major advantage over other methods in terms of memory requirements (up ...
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IEEEUSA EBooks

This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3D orthogonal matrix, leading to the discussion of particle and rigid body dynamics. The book continues with the eigenvalue problem and its application to multi variable vibrations. Because the eigenvalue problem requires some operations with polynomials, a separate discussion of these is given in an appendix. The example of the vibrating string is given with a comparison of the matrix analysis to the cont nuous solution. Table of Contents: Matrix Fundamentals / Determinants / Matrix Inversion / Linear Simultaneous Equation Sets / Orthogonal Transforms / Matrix Eigenvalue Analysis / Matrix Analysis of Vibrating Systems

Some Linear Algebra Fundamentals
This chapter contains sections titled: Notations and Definitions Operators and Functions Norms Decompositions MoorePenrose Pseudoinverse Idempotent Matrices Kronecker Algebra Isomorphism between Complex and Real Matrices Derivatives Inner Product GramSchmidt Orthogonalization Calculating the Roots of Polynomials Sensitivity of the Least Squares Solution Exercises Appendix

From the early pulse code modulationbased coders to some of the recent multi rate wideband speech coding standards, the area of speech coding made several significant strides with an objective to attain high quality of speech at the lowest possible bit rate. This book presents some of the recent advances in linear prediction (LP)based speech analysis that employ perceptual models for narrow and wideband speech coding. The LP analysissynthesis framework has been successful for speech coding because it fits well the sourcesystem paradigm for speech synthesis. Limitations associated with the conventional LP have been studied extensively, and several extensions to LPbased analysis synthesis have been proposed, e.g., the discrete allpole modeling, the perceptual LP, the warped LP, the LP with modified filter structures, the IIR based pure LP, allpole modeling using the weightedsum of LSP polynomials, the LP for low frequency emphasis, and the cascadeform LP. These extensions can be classified as algorithms that either attempt to improve the LP spectral envelope fitting performance or embed perceptual models in the LP. The first half of the book reviews some of the recent developments in predictive modeling of speech with the help of Matlab™ Simulation examples. Advantages of integrating perceptual models in low bit rate speech coding depend on the accuracy of these models to mimic the human performance and, more importantly, on the achievable "coding gains" and "computational overhead" associated with these physiological models. Methods that exploit the masking properties of the human ear in speech coding standards, even today, are largely based on concepts introduced by Schroeder and Atal in 1979. For example, a simple approach employed in speech coding standards is to use a perceptual weighting filter to shape the quantization noise according to the masking properties of the human ear. The second half of the book reviews some of the recent developmen s in perceptual modeling of speech (e.g., masking threshold, psychoacoustic models, auditory excitation pattern, and loudness) with the help of Matlab™ simulations. Supplementary material including Matlab™ programs and simulation examples presented in this book can also be accessed here. Table of Contents: Introduction / Predictive Modeling of Speech / Perceptual Modeling of Speech

This chapter contains sections titled: Problems

This chapter contains sections titled: Vectors and Matrices Gaussian Random Variables Correlation Functions MeanSquare Parameter Estimation Polynomials Notes and References Problems Computer Exercises

Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the CayleyHamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finitedimensional vector space over the field of complex numbers C, and let T : V > V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: Let A be a square matrix with complex entries. Then A is similar to a matrix J in Jordan Canonical Form, i.e., there is an invertible matrix P nd a matrix J in Jordan Canonical Form with A = PJP1. We further present an algorithm to find P and J, assuming that one can factor the characteristic polynomial of A. In developing this algorithm we introduce the eigenstructure picture (ESP) of a matrix, a pictorial representation that makes JCF clear. The ESP of A determines J, and a refinement, the labeled eigenstructure picture (ℓESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader.

Potential Fields in Three Dimensions
This chapter contains sections titled: The field of a charge, Legendre polynomials, Spherical Harmonics, The Field Due to Arbitrary Distribution of Charge, Translation Operators and Error Bounds, The Fast Multipole Algorithm

In this lecture, we study Bezier and Bspline curves and surfaces, mathematical representations for freeform curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bezier/Bsplines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bezier and Bspline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, Bspline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of Bspline curves, NURBS curves, and triangu ar and tensor product surfaces.

Solution of Algebraic Equations
This chapter deals with the determination of limits of the roots of polynomials, including their separation. Three methods are considered, namely, Lagrange's method, the LobachevskiGraeffe method, and Bernoulli's method. In addition, the chapter talks about BiergeViete method and Lin methods. These are followed by applications.

C. Derivation of the Chebyshev Polynomials
First published in 1981, Robert S. Elliott's Antenna Theory and Design is one of the most significant works in electromagnetic theory and applications. In its broadranging, analytic treatment, replete with supporting experimental evidence, Antenna Theory and Design conveys fundamental methods of analysis that can be used to predict the electromagnetic behavior of nearly everything that radiates. After more than two decades, it remains a key resource for students, professors, researchers, and engineers who require a comprehensive, indepth treatment of the subject. In response to requests from many of our members, IEEE is now reissuing this classic. Newly revised, it once again will be an invaluable textbook and an enduring reference for practicing engineers. The IEEE Press Series on Electromagnetic Wave Theory offers outstanding coverage of the field. It consists of new titles of contemporary interest as well as reissues and revisions of recognized classics by established authors and researchers. The series emphasizes works of longterm archival significance in electromagnetic waves and applications. Designed specifically for graduate students, researchers, and practicing engineers, the series provides affordable volumes that explore and explain electromagnetic waves beyond the undergraduate level.