000			05874cam a2200433Ii 4500
001			95681
003			ES-MaUEC
005			20230102112716.0
006			m o d
007			cr cnu---unuuu
008			170330s2017 sz a ob 001 0 eng d
020			_a3319536885 _q(electronic bk.)
020			_a9783319536880 _q(electronic bk.)
020			_z3319536877
020			_z9783319536873 _q(print)
040			_aGW5XE _cGW5XE _dEBLCP _dYDX _dOCLCF _dIOG _dSTF _dMERER _dESU _dOCLCQ _dJBG _dIAD _dICW _dICN _dCOO _dOTZ _dU3W _dES-MaUEC _bspa
050		4	_aQA161.P59 _bD865 2017 EB
100	1		_aDumitrescu, Bogdan, _eautor
245	1	0	_aPositive trigonometric polynomials and signal processing applications _cBogdan Dumitrescu.
250			_aSecond edition.
264		1	_aDordrecht _bSpringer _c2017.
300			_a1 recurso en línea (xvi, 276 páginas) _bilustraciones
336			_aTexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
490	0		_aSignals and communication technology _x1860-4862
500			_aSpringerLink _bSpringer Engineering eBooks 2017 English+International
504			_aIncluye referencias bibliográficas e índice
505	0		_aPreface; Contents; 1 Positive Polynomials; 1.1 Types of Polynomials; 1.2 Positive Polynomials; 1.3 Toeplitz Positivity Conditions; 1.4 Positivity on an Interval; 1.5 Details and Other Facts; 1.5.1 Chebyshev Polynomials; 1.5.2 Positive Polynomials in mathbbR[t] as Sum-of-Squares; 1.5.3 Proof of Theorem 1.11; 1.5.4 Proof of Theorem 1.13; 1.5.5 Proof of Theorem 1.15; 1.5.6 Proof of Theorem 1.17; 1.5.7 Proof of Theorem 1.18; 1.6 Bibliographical and Historical Notes; References; 2 Gram Matrix Representation; 2.1 Parameterization of Trigonometric Polynomials.
505	8		_a2.10.2 Cosine Polynomials and the DCT2.11 Fast Algorithms; 2.12 Details and Other Facts; 2.12.1 Writing Programs with Positive Trigonometric Polynomials; 2.12.2 Proof of Theorem 2.16; 2.12.3 Proof of Theorem 2.19; 2.12.4 Proof of Theorem 2.21; 2.13 Bibliographical and Historical Notes; References; 3 Multivariate Polynomials; 3.1 Multivariate Polynomials; 3.2 Sum-of-Squares Multivariate Polynomials; 3.3 Sum-of-Squares of Real Polynomials; 3.4 Gram Matrix Parameterization of Multivariate Trigonometric Polynomials; 3.5 Sum-of-Squares Relaxations; 3.5.1 Relaxation Principle; 3.5.2 A Case Study.
505	8		_a2.2 Optimization Using the Trace Parameterization2.3 Toeplitz Quadratic Optimization; 2.4 Duality; 2.5 Kalman -- Yakubovich -- Popov Lemma; 2.6 Spectral Factorization from a Gram Matrix; 2.6.1 SDP Computation of a Rank-1 Gram Matrix; 2.6.2 Spectral Factorization Using a Riccati Equation; 2.7 Parameterization of Real Polynomials; 2.8 Choosing the Right Basis; 2.8.1 Basis of Trigonometric Polynomials; 2.8.2 Transformation to Real Polynomials; 2.8.3 Gram-Pair Matrix Parameterization; 2.9 Interpolation Representations; 2.10 Mixed Representations; 2.10.1 Complex Polynomials and the DFT.
505	8		_a3.11.2 Pos3Poly Program with Multivariate Polynomials3.11.3 A CVX Program Using the Gram-Pair Parameterization; 3.12 Bibliographical and Historical Notes; References; 4 Polynomials Positive on Domains; 4.1 Real Polynomials Positive on Compact Domains; 4.2 Trigonometric Polynomials Positive on Frequency Domains; 4.2.1 Gram Set Parameterization; 4.2.2 Gram-Pair Set Parameterization; 4.3 Bounded Real Lemma; 4.3.1 Gram Set BRL; 4.3.2 BRL for Polynomials with Matrix Coefficients; 4.3.3 Gram-Pair Set BRL; 4.4 Positivstellensatz for Trigonometric Polynomials; 4.5 Proof of Theorem 4.11.
505	8		_a3.5.3 Optimality Certificate3.6 Gram Matrices from Partial Bases; 3.6.1 Sparse Polynomials and Gram Representation; 3.6.2 Relaxations; 3.7 Gram Matrices of Real Multivariate Polynomials; 3.7.1 Gram Parameterization; 3.7.2 Sum-of-Squares Relaxations; 3.7.3 Sparseness Treatment; 3.8 Pairs of Relaxations; 3.9 The Gram-Pair Parameterization; 3.9.1 Basic Gram-Pair Parameterization; 3.9.2 Parity Discussion; 3.9.3 LMI Form; 3.10 Polynomials with Matrix Coefficients; 3.11 Details and Other Facts; 3.11.1 Transformation Between Trigonometric and Real Nonnegative Polynomials.
520	3		_aThis revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers. < Features updated information on LMI parameterizations of sum-of-squares trigonometric polynomials; Contains applications in optimization of 1-D and 2-D filter design, orthogonal filterbanks; Includes a new chapter dedicated to applications in super-resolution theory that connects to a currently very active research area.
650		7	_aPolinomios _2embne _0(OCoLC)fst01070715 _0 _9669509
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=http://link.springer.com/10.1007/978-3-319-53688-0 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
988			_aEBOOK, asignarmaterias, EBSPRINGER_2017C
998			_b02/2018 _dz _e- _zSI
999			_c95681 _d95681 _x1