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Preface; Acknowledgements; Contents; Contributors; About the Editors; Part I Theory; Optimal Control of Partial Differential Equations; 1 Introduction; 2 Setting of the Model Control Problem; 3 Existence of a Solution; 4 Some Other Control Problems; 4.1 The Linear Quadratic Control Problem; 4.2 A Neumann Boundary Control Problem; 4.3 A Dirichlet Boundary Control Problem; 4.4 A Parabolic Control Problem; 4.5 A Problem with State Constraints; 5 First Order Optimality Conditions; 6 Second Order Optimality Conditions; 7 Numerical Approximation; 8 Convergence of the Approximations
9 Error Estimates10 Piecewise Linear Approximations of the Controls; 11 Semidiscretization of the Problem (P); 12 Superconvergence and Postprocessing Step; 13 Time Dependent Problems; 14 An Optimization Method; 15 An Example; References; Introduction to First-Principle Simulation of Molecular Systems; 1 Introduction; 2 Optimization in Hilbert Spaces; 3 Introduction to the Spectral Theory of Self-adjoint Operators; 3.1 Linear Operators on Hilbert Spaces; 3.2 Spectrum; 4 The Quantum Many-Body Problem; 4.1 One-Particle Systems; 4.2 Many-Particle Systems; 5 First-Principle Molecular Simulation
6 Hartree-Fock Approximation7 Numerical Approximation of Eigenvalues of Self-adjoint Operators; References; Accurate Computations and Applications of Some Classesof Matrices; 1 Introduction; 2 Errors and High Relative Accuracy; 3 P-Matrices, M-Matrices, Diagonal Dominance and Applications to LC Problems; 4 HRA for Diagonally Dominant M-Matrices; 5 Totally Positive Matrices and Bidiagonal Factorizations; 5.1 Neville Elimination and Bidiagonal Factorizations; 5.2 HRA for SBD Matrices; 6 Applications of Totally Positive Matrices to CAGD; 7 HRA for Some Subclasses of TP Matrices
7.1 HRA with Rational Bernstein-Vandermonde Matrices7.2 HRA with q-Bernstein-Vandermonde Matrices; 7.3 HRA with Jacobi-Stirling Matrices; References; Introduction to Communication Avoiding Algorithms for Direct Methods of Factorization in Linear Algebra; 1 Introduction; 1.1 Communication Avoiding Algorithms; 1.2 Different Previous Approaches for Reducing Communication; 1.3 Notations; 2 Lower Bounds on Communication for Dense Linear Algebra; 3 Communication Avoiding LU Factorization; 3.1 Parallel Block LU Factorization; 3.2 Tournament Pivoting; 3.3 Pivoting Strategies and Numerical Stability
3.4 Selection of References for LU Factorization4 Communication Avoiding QR Factorization; 4.1 Communication Avoiding QR Factorization for a Tall and Skinny Matrix: TSQR; 4.2 Communication Avoiding QR Factorization; 5 Communication Avoiding Rank Revealing Factorization and Low Rank Matrix Approximation; 5.1 Rank Revealing QR Factorization; 5.2 Tournament Pivoting for Selecting a Set of k Columns; 5.3 Low Rank Matrix Approximation for Sparse Matrices; References; Part II Applications; Singular Traveling Waves and Non-linear Reaction-DiffusionEquations; 1 Pattern Formation in Morphogenesis; 2 Nonlinear Reaction-Diffusion Models.
9 Error Estimates10 Piecewise Linear Approximations of the Controls; 11 Semidiscretization of the Problem (P); 12 Superconvergence and Postprocessing Step; 13 Time Dependent Problems; 14 An Optimization Method; 15 An Example; References; Introduction to First-Principle Simulation of Molecular Systems; 1 Introduction; 2 Optimization in Hilbert Spaces; 3 Introduction to the Spectral Theory of Self-adjoint Operators; 3.1 Linear Operators on Hilbert Spaces; 3.2 Spectrum; 4 The Quantum Many-Body Problem; 4.1 One-Particle Systems; 4.2 Many-Particle Systems; 5 First-Principle Molecular Simulation
6 Hartree-Fock Approximation7 Numerical Approximation of Eigenvalues of Self-adjoint Operators; References; Accurate Computations and Applications of Some Classesof Matrices; 1 Introduction; 2 Errors and High Relative Accuracy; 3 P-Matrices, M-Matrices, Diagonal Dominance and Applications to LC Problems; 4 HRA for Diagonally Dominant M-Matrices; 5 Totally Positive Matrices and Bidiagonal Factorizations; 5.1 Neville Elimination and Bidiagonal Factorizations; 5.2 HRA for SBD Matrices; 6 Applications of Totally Positive Matrices to CAGD; 7 HRA for Some Subclasses of TP Matrices
7.1 HRA with Rational Bernstein-Vandermonde Matrices7.2 HRA with q-Bernstein-Vandermonde Matrices; 7.3 HRA with Jacobi-Stirling Matrices; References; Introduction to Communication Avoiding Algorithms for Direct Methods of Factorization in Linear Algebra; 1 Introduction; 1.1 Communication Avoiding Algorithms; 1.2 Different Previous Approaches for Reducing Communication; 1.3 Notations; 2 Lower Bounds on Communication for Dense Linear Algebra; 3 Communication Avoiding LU Factorization; 3.1 Parallel Block LU Factorization; 3.2 Tournament Pivoting; 3.3 Pivoting Strategies and Numerical Stability
3.4 Selection of References for LU Factorization4 Communication Avoiding QR Factorization; 4.1 Communication Avoiding QR Factorization for a Tall and Skinny Matrix: TSQR; 4.2 Communication Avoiding QR Factorization; 5 Communication Avoiding Rank Revealing Factorization and Low Rank Matrix Approximation; 5.1 Rank Revealing QR Factorization; 5.2 Tournament Pivoting for Selecting a Set of k Columns; 5.3 Low Rank Matrix Approximation for Sparse Matrices; References; Part II Applications; Singular Traveling Waves and Non-linear Reaction-DiffusionEquations; 1 Pattern Formation in Morphogenesis; 2 Nonlinear Reaction-Diffusion Models.