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MARC Lista (tabellare)
Esercizi di analisi numerica matriciale e di ottimizzazione / P. G. Ciarlet, B. Miara, J. M. Thomas ; ed. italiana a cura di Claudio Canuto ; traduzione di Claudia Manotti
Esercizi di analisi numerica matriciale e di ottimizzazione / P. G. Ciarlet, B. Miara, J. M. Thomas ; ed. italiana a cura di Claudio Canuto ; traduzione di Claudia Manotti
Autore Ciarlet, Philippe G. <1938->
Pubbl/distr/stampa Milano [etc.], : Masson, 1989
Descrizione fisica XIII, 144 p. ; 24 cm.
Disciplina 512.9434
Altri autori (Persone) Miara, Bernadette
Thomas, John Meurig
Collana Collana di matematica applicata e numerica
Soggetto topico Matrici algebriche - Esercizi
Analisi numerica - Esercizi
Ottimizzazione
ISBN 8821406393
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione ita
Titolo uniforme
Record Nr. UNISANNIO-CFI0205669
Ciarlet, Philippe G. <1938->  
Milano [etc.], : Masson, 1989
Materiale a stampa
Lo trovi qui: Univ. del Sannio
Opac: Controlla la disponibilità qui
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications [[electronic resource] ] : Cetraro, Italy 2015 / / by Michele Benzi, Dario Bini, Daniel Kressner, Hans Munthe-Kaas, Charles Van Loan ; edited by Michele Benzi, Valeria Simoncini
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications [[electronic resource] ] : Cetraro, Italy 2015 / / by Michele Benzi, Dario Bini, Daniel Kressner, Hans Munthe-Kaas, Charles Van Loan ; edited by Michele Benzi, Valeria Simoncini
Autore Benzi Michele
Edizione [1st ed. 2016.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Descrizione fisica 1 online resource (IX, 406 p. 57 illus., 46 illus. in color.)
Disciplina 512.9434
Collana C.I.M.E. Foundation Subseries
Soggetto topico Numerical analysis
Computer mathematics
Numerical Analysis
Computational Science and Engineering
ISBN 3-319-49887-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Acknowledgments -- Contents -- Structured Matrix Problems from Tensors -- 1 Introduction -- 2 The Exploitation of Structure in Matrix Computations -- 2.1 Exploiting Data Sparsity -- 2.2 Exploiting Structured Eigensystems -- 2.3 Exploiting the Right Representation -- 2.4 Exploiting Orthogonality Structures -- 2.5 Exploiting a Structured Data layout -- 3 Matrix-Tensor Connections -- 3.1 Talking About Tensors -- 3.2 Tensor Parts: Fibers and Slices -- 3.3 Order-4 Tensors and Block Matrices -- 3.4 Modal Unfoldings -- 3.5 The vec Operation -- 3.6 The Kronecker Product -- 3.7 Perfect Shuffles, Kronecker Products, and Transposition -- 3.8 Tensor Notation -- 3.9 The Tensor Product -- 4 A Rank-1 Tensor Problem -- 4.1 Rank-1 Matrices -- 4.2 Rank-1 Tensors -- 4.3 The Nearest Rank-1 Problem for Matrices -- 4.4 A Nearest Rank-1 Tensor Problem -- 5 The Variational Approach to Tensor Singular Values -- 5.1 Rayleigh Quotient/Power Method Ideas: The Matrix Case -- 5.2 Rayleigh Quotient/Power Method Ideas: The Tensor Case -- 5.3 A First Look at Tensor Rank -- 6 Tensor Symmetry -- 6.1 Tensor Transposition -- 6.2 Symmetric Tensors -- 6.3 Symmetric Rank -- 6.4 The Eigenvalues of a Symmetric Tensor -- 6.5 Symmetric Embeddings -- 7 The Tucker Decomposition -- 7.1 Tucker Representations: The Matrix Case -- 7.2 Tucker Representations: The Tensor Case -- 7.3 The Mode-k Product -- 7.4 The Core Tensor -- 7.5 The Higher-Order SVD -- 7.6 The Tucker Nearness Problem -- 7.7 A Jacobi Approach -- 8 The CP Decomposition -- 8.1 CP Representations: The Matrix Case -- 8.2 CP Representation: The Tensor Case -- 8.3 More About Tensor Rank -- 8.4 The Nearest CP Problem -- 8.5 The Khatri-Rao Product -- 8.6 Equivalent Formulations -- 9 The Kronecker Product SVD -- 9.1 The Nearest Kronecker Product Problem -- 9.2 The Kronecker Product SVD (KPSVD).
9.3 Order-4 Tensor Approximation Using the KPSVD -- 10 The Tensor Train SVD -- 10.1 Tensor Trains and Data Sparsity -- 10.2 Computing an SVD-Based Tensor Train Representation -- 11 Tensor Problems with Multiple Symmetries -- 11.1 A First Look at Multiple Symmetries -- 11.2 A Tensor Problem with Multiple Symmetries -- 11.3 Perfect Shuffle Symmetry -- 11.4 Block Diagonalization -- 11.5 Low-Rank PS-Symmetric Approximation -- References -- Matrix Structures in Queuing Models -- 1 Introduction to Matrix Structures -- 1.1 Some Examples of Matrix Structures -- 2 Structures Encountered in Queuing Models -- 2.1 Markov Chains -- 2.2 Some Examples -- 2.3 Other Structures -- 3 Fundamentals on Structured Matrices -- 3.1 Classical Results on Toeplitz Matrices -- 3.2 Toeplitz Matrices, Polynomials and Power Series -- 3.3 Toeplitz Matrices, Trigonometric Algebras, and FFT -- 3.3.1 Circulant Matrices -- 3.3.2 z-Circulant Matrices -- 3.3.3 Matrix Embedding -- 3.3.4 Triangular Toeplitz Matrices -- 3.3.5 z-Circulant and Triangular Toeplitz Matrices -- 3.3.6 Other Matrix Algebras -- 3.4 Displacement Operators -- 3.4.1 Other Operators: Cauchy-Like Matrices -- 3.5 Algorithms for Toeplitz Inversion -- 3.5.1 Super-Fast Toeplitz Solvers -- 3.6 Asymptotic Spectral Properties and Preconditioning -- 3.6.1 Trigonometric Matrix Algebras and Preconditioning -- 3.7 Rank Structures -- 3.8 Bibliographical Notes -- 4 Algorithms for Structured Markov Chains: The Finite Case -- 4.1 The Block Tridiagonal Case -- 4.2 The Case of a Block Hessenberg Matrix -- 4.3 Applicability of CR -- 4.4 A Functional Interpretation of Cyclic Reduction -- 4.4.1 Convergence Properties When 1{ξm,ξm+1} -- 4.5 A Special Case: Non-skip-Free Markov Chain -- 4.6 A Special Case: QBD with Tridiagonal Blocks -- 5 Algorithms for Structured Markov Chains: The Infinite Case -- 5.1 M/G/1-Type Markov Chains.
5.2 G/M/1-Type Markov Chains -- 5.3 QBD Markov Chains -- 5.4 Computing Matrices G and R: The Weak Canonical Factorization -- 5.4.1 Solving Matrix Equations -- 5.4.2 Solving Matrix Equations by Means of CR: The QBD Case -- 5.4.3 Solving Matrix Equations by Means of CR: The M/G/1 and G/M/1 Cases -- 5.5 Shifting Techniques -- 5.5.1 Shift to the Right -- 5.6 Shift to the Left -- 5.7 Double Shift -- 5.8 Shifts and Canonical Factorizations -- 5.9 Available Software -- 6 Other Problems -- 6.1 Tree-Like Processes -- 6.2 Vector Equations -- 6.2.1 An Optimistic Approach -- 7 Exponential of a Block Triangular Block Toeplitz Matrix -- 7.1 Using ε-Circulant Matrices -- 7.2 Using Circulant Matrices -- 7.3 Method Based on Taylor Expansion -- References -- Matrices with Hierarchical Low-Rank Structures -- 1 Introduction -- 1.1 Sparsity Versus Data-Sparsity -- 1.2 Applications of Hierarchical Low-Rank Structures -- 1.3 Outline -- 2 Low-Rank Approximation -- 2.1 The SVD and Best Low-Rank Approximation -- 2.2 Stability of SVD and Low-Rank Approximation -- 2.3 Algorithms for Low-Rank Approximation -- 2.3.1 SVD-Based Algorithms -- 2.3.2 Lanczos-Based Algorithms -- 2.3.3 Randomized Algorithms -- 2.3.4 Adaptive Cross Approximation (ACA) -- 2.4 A Priori Approximation Results -- 2.4.1 Separability and Low Rank -- 2.4.2 Low Rank Approximation via Semi-separable Approximation -- 3 Partitioned Low-Rank Structures -- 3.1 HODLR Matrices -- 3.1.1 Matrix-Vector Multiplication -- 3.1.2 Matrix Addition -- 3.1.3 Matrix Multiplication -- 3.1.4 Matrix Factorization and Linear Systems -- 3.2 General Clustering Strategies -- 3.2.1 Geometrical Clustering -- 3.2.2 Algebraic Clustering -- 3.3 H-Matrices -- 3.4 Approximation of Elliptic Boundary Value Problems by H-Matrices -- 4 Partitioned Low-Rank Structures with Nested Low-Rank Representations -- 4.1 HSS Matrices -- 4.2 H2-Matrices.
References -- Localization in Matrix Computations: Theory and Applications -- 1 Introduction -- 1.1 Localization in Physics -- 1.2 Localization in Numerical Mathematics -- 2 Notation and Background in Linear Algebra and Graph Theory -- 3 Localization in Matrix Functions -- 3.1 Matrices with Decay -- 3.2 Decay Bounds for the Inverse -- 3.3 Decay Bounds for the Matrix Exponential -- 3.4 Decay Bounds for General Analytic Functions -- 3.4.1 Bounds for the Normal Case -- 3.4.2 Bounds for the Nonnormal Case -- 3.5 Bounds for Matrix Functions Defined by Integral Transforms -- 3.6 Functions of Structured Matrices -- 3.7 Some Generalizations -- 3.7.1 The Time-Ordered Exponential -- 3.8 Decal Algebras -- 3.9 Localization in Matrix Factorizations -- 3.10 Localization in the Unbounded Case -- 4 Applications -- 4.1 Applications in Numerical Linear Algebra -- 4.1.1 Linear Systems with Localized Solutions -- 4.1.2 Construction of Preconditioners -- 4.1.3 Localization and Eigenvalue Problems -- 4.1.4 Approximation of Matrix Functions -- 4.1.5 Approximation Based on Quadrature Rules -- 4.1.6 Error Bounds for Krylov Subspace Approximations -- 4.1.7 Exponentials of Stochastic Matrices -- 4.1.8 Exponential Integrators -- 4.2 Linear Scaling Methods for Electronic Structure Computations -- 4.3 Further Applications -- 4.3.1 Localized Solutions to Matrix Equations -- 4.3.2 Localization in Graph and Network Analysis -- 4.3.3 Log-Determinant Evaluation -- 4.3.4 Quantum Information Theory -- 5 Conclusions and Future Work -- References -- Groups and Symmetries in Numerical Linear Algebra -- 1 Introduction -- 1.1 Motivation for the Main Topics of the Lectures -- 2 Prelude: Introduction to Group Theory -- 2.1 Groups and Actions -- 2.2 Subgroups and Quotients -- 2.3 Homomorphisms and Exact Sequences -- 2.4 Products of Groups and Split Exact Sequences.
2.5 Domains in Computational Mathematics -- 3 Abelian Groups, Fourier Analysis, Lattices and Sampling -- 3.1 Introduction to Abelian Groups -- 3.1.1 Definition and Basic Properties -- 3.1.2 Topology -- 3.1.3 The Elementary Groups -- 3.2 Computing with FGAs -- 3.2.1 Abelian Categories -- 3.2.2 Free FGAs and Smith's Normal Form -- 3.2.3 General Homomorphisms -- 3.2.4 Hermite's Normal Form -- 3.2.5 Summary -- 3.3 Circulant Matrices and the Discrete Fourier Transform -- 3.4 Fourier Analysis on General LCAs -- 3.4.1 Functions on G -- 3.4.2 Shifts, Integrals and Convolutions -- 3.4.3 The Dual Group -- 3.4.4 The Fourier Transform -- 3.4.5 Schwartz Space and Tempered Distributions -- 3.4.6 Pullback and Pushforward of Functions on Groups -- 3.5 Duality of Subgroups and Quotients -- 3.5.1 Dual Homomorphisms -- 3.5.2 The Fundamental Duality Theorem -- 3.6 Lattices and Sampling -- 3.6.1 Pullback and Pushforward on Lattices -- 3.6.2 Choosing Coset Representatives -- 3.6.3 Sampling and Aliasing -- 3.7 The Fast Fourier Transform (FFT) -- 3.7.1 Heisenberg Groups and the Weil-Brezin Map -- 3.8 Lattice Rules -- 3.8.1 Computational Fourier Analysis on Rd -- 3.8.2 Eigenfunctions of the Continuous and Discrete Fourier Transforms -- 3.9 Boundaries, Mirrors and Kaleidoscopes -- 3.10 Cyclic Reduction -- 3.11 Preconditioning with Convolutional Operators -- 3.11.1 Matrix Multiplication by Diagonals -- 3.11.2 Preconditioning -- 4 Domain Symmetries and Non-commutative Groups -- 4.1 G-Equivariant Matrices -- 4.2 The Group Algebra -- 4.3 The Generalized Fourier Transform (GFT) -- 4.4 Applications to the Matrix Exponential -- 4.4.1 Example: Equilateral Triangle -- 4.4.2 Example: Icosahedral Symmetry -- 5 Concluding Remarks -- References.
Record Nr. UNINA-9910166058103321
Benzi Michele  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications [[electronic resource] ] : Cetraro, Italy 2015 / / by Michele Benzi, Dario Bini, Daniel Kressner, Hans Munthe-Kaas, Charles Van Loan ; edited by Michele Benzi, Valeria Simoncini
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications [[electronic resource] ] : Cetraro, Italy 2015 / / by Michele Benzi, Dario Bini, Daniel Kressner, Hans Munthe-Kaas, Charles Van Loan ; edited by Michele Benzi, Valeria Simoncini
Autore Benzi Michele
Edizione [1st ed. 2016.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Descrizione fisica 1 online resource (IX, 406 p. 57 illus., 46 illus. in color.)
Disciplina 512.9434
Collana C.I.M.E. Foundation Subseries
Soggetto topico Numerical analysis
Computer mathematics
Numerical Analysis
Computational Science and Engineering
ISBN 3-319-49887-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Acknowledgments -- Contents -- Structured Matrix Problems from Tensors -- 1 Introduction -- 2 The Exploitation of Structure in Matrix Computations -- 2.1 Exploiting Data Sparsity -- 2.2 Exploiting Structured Eigensystems -- 2.3 Exploiting the Right Representation -- 2.4 Exploiting Orthogonality Structures -- 2.5 Exploiting a Structured Data layout -- 3 Matrix-Tensor Connections -- 3.1 Talking About Tensors -- 3.2 Tensor Parts: Fibers and Slices -- 3.3 Order-4 Tensors and Block Matrices -- 3.4 Modal Unfoldings -- 3.5 The vec Operation -- 3.6 The Kronecker Product -- 3.7 Perfect Shuffles, Kronecker Products, and Transposition -- 3.8 Tensor Notation -- 3.9 The Tensor Product -- 4 A Rank-1 Tensor Problem -- 4.1 Rank-1 Matrices -- 4.2 Rank-1 Tensors -- 4.3 The Nearest Rank-1 Problem for Matrices -- 4.4 A Nearest Rank-1 Tensor Problem -- 5 The Variational Approach to Tensor Singular Values -- 5.1 Rayleigh Quotient/Power Method Ideas: The Matrix Case -- 5.2 Rayleigh Quotient/Power Method Ideas: The Tensor Case -- 5.3 A First Look at Tensor Rank -- 6 Tensor Symmetry -- 6.1 Tensor Transposition -- 6.2 Symmetric Tensors -- 6.3 Symmetric Rank -- 6.4 The Eigenvalues of a Symmetric Tensor -- 6.5 Symmetric Embeddings -- 7 The Tucker Decomposition -- 7.1 Tucker Representations: The Matrix Case -- 7.2 Tucker Representations: The Tensor Case -- 7.3 The Mode-k Product -- 7.4 The Core Tensor -- 7.5 The Higher-Order SVD -- 7.6 The Tucker Nearness Problem -- 7.7 A Jacobi Approach -- 8 The CP Decomposition -- 8.1 CP Representations: The Matrix Case -- 8.2 CP Representation: The Tensor Case -- 8.3 More About Tensor Rank -- 8.4 The Nearest CP Problem -- 8.5 The Khatri-Rao Product -- 8.6 Equivalent Formulations -- 9 The Kronecker Product SVD -- 9.1 The Nearest Kronecker Product Problem -- 9.2 The Kronecker Product SVD (KPSVD).
9.3 Order-4 Tensor Approximation Using the KPSVD -- 10 The Tensor Train SVD -- 10.1 Tensor Trains and Data Sparsity -- 10.2 Computing an SVD-Based Tensor Train Representation -- 11 Tensor Problems with Multiple Symmetries -- 11.1 A First Look at Multiple Symmetries -- 11.2 A Tensor Problem with Multiple Symmetries -- 11.3 Perfect Shuffle Symmetry -- 11.4 Block Diagonalization -- 11.5 Low-Rank PS-Symmetric Approximation -- References -- Matrix Structures in Queuing Models -- 1 Introduction to Matrix Structures -- 1.1 Some Examples of Matrix Structures -- 2 Structures Encountered in Queuing Models -- 2.1 Markov Chains -- 2.2 Some Examples -- 2.3 Other Structures -- 3 Fundamentals on Structured Matrices -- 3.1 Classical Results on Toeplitz Matrices -- 3.2 Toeplitz Matrices, Polynomials and Power Series -- 3.3 Toeplitz Matrices, Trigonometric Algebras, and FFT -- 3.3.1 Circulant Matrices -- 3.3.2 z-Circulant Matrices -- 3.3.3 Matrix Embedding -- 3.3.4 Triangular Toeplitz Matrices -- 3.3.5 z-Circulant and Triangular Toeplitz Matrices -- 3.3.6 Other Matrix Algebras -- 3.4 Displacement Operators -- 3.4.1 Other Operators: Cauchy-Like Matrices -- 3.5 Algorithms for Toeplitz Inversion -- 3.5.1 Super-Fast Toeplitz Solvers -- 3.6 Asymptotic Spectral Properties and Preconditioning -- 3.6.1 Trigonometric Matrix Algebras and Preconditioning -- 3.7 Rank Structures -- 3.8 Bibliographical Notes -- 4 Algorithms for Structured Markov Chains: The Finite Case -- 4.1 The Block Tridiagonal Case -- 4.2 The Case of a Block Hessenberg Matrix -- 4.3 Applicability of CR -- 4.4 A Functional Interpretation of Cyclic Reduction -- 4.4.1 Convergence Properties When 1{ξm,ξm+1} -- 4.5 A Special Case: Non-skip-Free Markov Chain -- 4.6 A Special Case: QBD with Tridiagonal Blocks -- 5 Algorithms for Structured Markov Chains: The Infinite Case -- 5.1 M/G/1-Type Markov Chains.
5.2 G/M/1-Type Markov Chains -- 5.3 QBD Markov Chains -- 5.4 Computing Matrices G and R: The Weak Canonical Factorization -- 5.4.1 Solving Matrix Equations -- 5.4.2 Solving Matrix Equations by Means of CR: The QBD Case -- 5.4.3 Solving Matrix Equations by Means of CR: The M/G/1 and G/M/1 Cases -- 5.5 Shifting Techniques -- 5.5.1 Shift to the Right -- 5.6 Shift to the Left -- 5.7 Double Shift -- 5.8 Shifts and Canonical Factorizations -- 5.9 Available Software -- 6 Other Problems -- 6.1 Tree-Like Processes -- 6.2 Vector Equations -- 6.2.1 An Optimistic Approach -- 7 Exponential of a Block Triangular Block Toeplitz Matrix -- 7.1 Using ε-Circulant Matrices -- 7.2 Using Circulant Matrices -- 7.3 Method Based on Taylor Expansion -- References -- Matrices with Hierarchical Low-Rank Structures -- 1 Introduction -- 1.1 Sparsity Versus Data-Sparsity -- 1.2 Applications of Hierarchical Low-Rank Structures -- 1.3 Outline -- 2 Low-Rank Approximation -- 2.1 The SVD and Best Low-Rank Approximation -- 2.2 Stability of SVD and Low-Rank Approximation -- 2.3 Algorithms for Low-Rank Approximation -- 2.3.1 SVD-Based Algorithms -- 2.3.2 Lanczos-Based Algorithms -- 2.3.3 Randomized Algorithms -- 2.3.4 Adaptive Cross Approximation (ACA) -- 2.4 A Priori Approximation Results -- 2.4.1 Separability and Low Rank -- 2.4.2 Low Rank Approximation via Semi-separable Approximation -- 3 Partitioned Low-Rank Structures -- 3.1 HODLR Matrices -- 3.1.1 Matrix-Vector Multiplication -- 3.1.2 Matrix Addition -- 3.1.3 Matrix Multiplication -- 3.1.4 Matrix Factorization and Linear Systems -- 3.2 General Clustering Strategies -- 3.2.1 Geometrical Clustering -- 3.2.2 Algebraic Clustering -- 3.3 H-Matrices -- 3.4 Approximation of Elliptic Boundary Value Problems by H-Matrices -- 4 Partitioned Low-Rank Structures with Nested Low-Rank Representations -- 4.1 HSS Matrices -- 4.2 H2-Matrices.
References -- Localization in Matrix Computations: Theory and Applications -- 1 Introduction -- 1.1 Localization in Physics -- 1.2 Localization in Numerical Mathematics -- 2 Notation and Background in Linear Algebra and Graph Theory -- 3 Localization in Matrix Functions -- 3.1 Matrices with Decay -- 3.2 Decay Bounds for the Inverse -- 3.3 Decay Bounds for the Matrix Exponential -- 3.4 Decay Bounds for General Analytic Functions -- 3.4.1 Bounds for the Normal Case -- 3.4.2 Bounds for the Nonnormal Case -- 3.5 Bounds for Matrix Functions Defined by Integral Transforms -- 3.6 Functions of Structured Matrices -- 3.7 Some Generalizations -- 3.7.1 The Time-Ordered Exponential -- 3.8 Decal Algebras -- 3.9 Localization in Matrix Factorizations -- 3.10 Localization in the Unbounded Case -- 4 Applications -- 4.1 Applications in Numerical Linear Algebra -- 4.1.1 Linear Systems with Localized Solutions -- 4.1.2 Construction of Preconditioners -- 4.1.3 Localization and Eigenvalue Problems -- 4.1.4 Approximation of Matrix Functions -- 4.1.5 Approximation Based on Quadrature Rules -- 4.1.6 Error Bounds for Krylov Subspace Approximations -- 4.1.7 Exponentials of Stochastic Matrices -- 4.1.8 Exponential Integrators -- 4.2 Linear Scaling Methods for Electronic Structure Computations -- 4.3 Further Applications -- 4.3.1 Localized Solutions to Matrix Equations -- 4.3.2 Localization in Graph and Network Analysis -- 4.3.3 Log-Determinant Evaluation -- 4.3.4 Quantum Information Theory -- 5 Conclusions and Future Work -- References -- Groups and Symmetries in Numerical Linear Algebra -- 1 Introduction -- 1.1 Motivation for the Main Topics of the Lectures -- 2 Prelude: Introduction to Group Theory -- 2.1 Groups and Actions -- 2.2 Subgroups and Quotients -- 2.3 Homomorphisms and Exact Sequences -- 2.4 Products of Groups and Split Exact Sequences.
2.5 Domains in Computational Mathematics -- 3 Abelian Groups, Fourier Analysis, Lattices and Sampling -- 3.1 Introduction to Abelian Groups -- 3.1.1 Definition and Basic Properties -- 3.1.2 Topology -- 3.1.3 The Elementary Groups -- 3.2 Computing with FGAs -- 3.2.1 Abelian Categories -- 3.2.2 Free FGAs and Smith's Normal Form -- 3.2.3 General Homomorphisms -- 3.2.4 Hermite's Normal Form -- 3.2.5 Summary -- 3.3 Circulant Matrices and the Discrete Fourier Transform -- 3.4 Fourier Analysis on General LCAs -- 3.4.1 Functions on G -- 3.4.2 Shifts, Integrals and Convolutions -- 3.4.3 The Dual Group -- 3.4.4 The Fourier Transform -- 3.4.5 Schwartz Space and Tempered Distributions -- 3.4.6 Pullback and Pushforward of Functions on Groups -- 3.5 Duality of Subgroups and Quotients -- 3.5.1 Dual Homomorphisms -- 3.5.2 The Fundamental Duality Theorem -- 3.6 Lattices and Sampling -- 3.6.1 Pullback and Pushforward on Lattices -- 3.6.2 Choosing Coset Representatives -- 3.6.3 Sampling and Aliasing -- 3.7 The Fast Fourier Transform (FFT) -- 3.7.1 Heisenberg Groups and the Weil-Brezin Map -- 3.8 Lattice Rules -- 3.8.1 Computational Fourier Analysis on Rd -- 3.8.2 Eigenfunctions of the Continuous and Discrete Fourier Transforms -- 3.9 Boundaries, Mirrors and Kaleidoscopes -- 3.10 Cyclic Reduction -- 3.11 Preconditioning with Convolutional Operators -- 3.11.1 Matrix Multiplication by Diagonals -- 3.11.2 Preconditioning -- 4 Domain Symmetries and Non-commutative Groups -- 4.1 G-Equivariant Matrices -- 4.2 The Group Algebra -- 4.3 The Generalized Fourier Transform (GFT) -- 4.4 Applications to the Matrix Exponential -- 4.4.1 Example: Equilateral Triangle -- 4.4.2 Example: Icosahedral Symmetry -- 5 Concluding Remarks -- References.
Record Nr. UNISA-996466767603316
Benzi Michele  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Autore Bart Harm
Edizione [1st ed. 2008.]
Pubbl/distr/stampa Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Descrizione fisica 1 online resource (420 p.)
Disciplina 512.9434
Collana Linear Operators and Linear Systems
Soggetto topico Operator theory
Matrix theory
Algebra
Number theory
Operator Theory
Linear and Multilinear Algebras, Matrix Theory
Number Theory
Soggetto genere / forma Electronic books.
ISBN 1-281-14098-8
9786611140984
3-7643-8268-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions.
Record Nr. UNINA-9910458174203321
Bart Harm  
Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Autore Bart Harm
Edizione [1st ed. 2008.]
Pubbl/distr/stampa Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Descrizione fisica 1 online resource (420 p.)
Disciplina 512.9434
Collana Linear Operators and Linear Systems
Soggetto topico Operator theory
Matrix theory
Algebra
Number theory
Operator Theory
Linear and Multilinear Algebras, Matrix Theory
Number Theory
ISBN 1-281-14098-8
9786611140984
3-7643-8268-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions.
Record Nr. UNINA-9910784771703321
Bart Harm  
Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Factorization of Matrix and Operator Functions: The State Space Method [[electronic resource] /] / by Harm Bart, Israel Gohberg, Marinus A. Kaashoek, André C.M. Ran
Autore Bart Harm
Edizione [1st ed. 2008.]
Pubbl/distr/stampa Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Descrizione fisica 1 online resource (420 p.)
Disciplina 512.9434
Collana Linear Operators and Linear Systems
Soggetto topico Operator theory
Matrix theory
Algebra
Number theory
Operator Theory
Linear and Multilinear Algebras, Matrix Theory
Number Theory
ISBN 1-281-14098-8
9786611140984
3-7643-8268-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions.
Record Nr. UNINA-9910819549103321
Bart Harm  
Basel : , : Birkhäuser Basel : , : Imprint : Birkhäuser, , 2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Formal matrices [[electronic resource] /] / by Piotr Krylov, Askar Tuganbaev
Formal matrices [[electronic resource] /] / by Piotr Krylov, Askar Tuganbaev
Autore Krylov Piotr
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VIII, 156 p.)
Disciplina 512.9434
Collana Algebra and Applications
Soggetto topico Associative rings
Rings (Algebra)
Category theory (Mathematics)
Homological algebra
K-theory
Matrix theory
Algebra
Associative Rings and Algebras
Category Theory, Homological Algebra
K-Theory
Linear and Multilinear Algebras, Matrix Theory
ISBN 3-319-53907-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- Construction of Formal Matrix Rings of Order 2 -- Modules over Formal Matrix Rings -- Formal Matrix Rings over a Given Ring -- Grothendieck and Whitehead Groups of Formal Matrix Rings.
Record Nr. UNINA-9910254308803321
Krylov Piotr  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Functions of matrices : theory and computation / Nicholas J. Higham
Functions of matrices : theory and computation / Nicholas J. Higham
Autore Higham, Nicholas J.
Pubbl/distr/stampa Philadelphia : Society for industrial and applied mathematics, ©2008
Descrizione fisica XX, 425 p. : ill. ; 23 cm
Disciplina 512.9434
Soggetto non controllato Matrici
Algebra
ISBN 978-0-898716-46-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-990008783740403321
Higham, Nicholas J.  
Philadelphia : Society for industrial and applied mathematics, ©2008
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Functions of matrices : theory and computation / Nicholas J. Higham
Functions of matrices : theory and computation / Nicholas J. Higham
Autore Higham, Nicholas J.
Pubbl/distr/stampa Philadelphia : Society for Industrial and Applied Mathematics, c2008
Descrizione fisica xx, 425 p. : ill. ; 26 cm
Disciplina 512.9434
Soggetto topico Matrices
Functions
Factorization (Mathematics)
ISBN 9780898716467
Classificazione AMS 15-02
AMS 93B40
AMS 93C05
LC QA188.H53
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001717109707536
Higham, Nicholas J.  
Philadelphia : Society for Industrial and Applied Mathematics, c2008
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Fundamentals of matrix computations / David S. Watkins
Fundamentals of matrix computations / David S. Watkins
Autore WATKINS, David S.
Edizione [2. ed.]
Pubbl/distr/stampa New York, : Wiley-Interscience, 2002
Descrizione fisica Testo elettronico (PDF) (XIII, 620 p.)
Disciplina 512.9434
Collana Pure and applied mathematics
Soggetto topico Matrici algebriche
ISBN 9780471249719
Formato Risorse elettroniche
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996451649003316
WATKINS, David S.  
New York, : Wiley-Interscience, 2002
Risorse elettroniche
Lo trovi qui: Univ. di Salerno
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