Search Results - "eigenvalue"

Foundations of applied electrodynamics by Wen, Geyi

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Foundations of applied electrodynamics by Wen, Geyi

Subjects: An electronic book accessible through the World Wide Web; click to view

Exact treatment of finite-dimensional and infinite-dimensional quantum systems by Živković, Tomislav P. (Tomislav Predavač)

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Fundamentals of matrix analysis with applications / by Saff, E. B., 1944-, Snider, Arthur David

Subjects: An electronic book accessible through the World Wide Web; click to view

Exact treatment of finite-dimensional and infinite-dimensional quantum systems by Živković, Tomislav P. (Tomislav Predavač)

Subjects: An electronic book accessible through the World Wide Web; click to view

Fundamentals of matrix analysis with applications / by Saff, E. B., 1944-, Snider, Arthur David

Subjects: An electronic book accessible through the World Wide Web; click to view

Nonconservative stability problems of modern physics / by Kirillov, Oleg N., 1972-

Subjects: “…Eigenvalues.…”
An electronic book accessible through the World Wide Web; click to view

Nonconservative stability problems of modern physics / by Kirillov, Oleg N., 1972-

Subjects: “…Eigenvalues.…”
An electronic book accessible through the World Wide Web; click to view

Nonlinear Perron-Frobenius theory by Lemmens, Bas

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Nonlinear Perron-Frobenius theory by Lemmens, Bas

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Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization / by Gustafson, Karl

Subjects: “…Eigenvalues.…”
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Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization / by Gustafson, Karl

Subjects: “…Eigenvalues.…”
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Numerical structural analysis / by O'Hara, Steven E., Ramming, Carisa H.

Table of Contents: “…Solutions of simultaneous linear algebraic equations using matrix algebra -- 2.1 Simultaneous equations -- 2.2 Matrices -- 2.3 Matrix operations -- 2.4 Cramer's rule -- 2.5 Method of adjoints or cofactor method -- 2.6 Gaussian elimination method -- 2.7 Gauss-Jordan elimination method -- 2.8 Improved Gauss-Jordan elimination method -- 2.9 Cholesky decomposition method -- 2.10 Error equations -- 2.11 Matrix inversion method -- 2.12 Gauss-Seidel iteration method -- 2.13 Eigenvalues by Cramer's rule -- 2.14 Faddeev-Leverrier method -- 2.15 Power method or iteration method -- References --…”
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Numerical structural analysis / by O'Hara, Steven E., Ramming, Carisa H.

Table of Contents: “…Solutions of simultaneous linear algebraic equations using matrix algebra -- 2.1 Simultaneous equations -- 2.2 Matrices -- 2.3 Matrix operations -- 2.4 Cramer's rule -- 2.5 Method of adjoints or cofactor method -- 2.6 Gaussian elimination method -- 2.7 Gauss-Jordan elimination method -- 2.8 Improved Gauss-Jordan elimination method -- 2.9 Cholesky decomposition method -- 2.10 Error equations -- 2.11 Matrix inversion method -- 2.12 Gauss-Seidel iteration method -- 2.13 Eigenvalues by Cramer's rule -- 2.14 Faddeev-Leverrier method -- 2.15 Power method or iteration method -- References --…”
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Numerical analysis / by Burden, Richard L.

Table of Contents: “…Mathematical preliminaries and error analysis -- Solutions of equations in one variable -- Interpolation and polynomial approximation -- Numerical differentiation and integration -- Initial-value problems for ordinary differential equations --Direct methods for solving linear systems -- Iterative techniques in matrix algebra -- Approximation theory -- Approximating eigenvalues -- Numerical solutions of nonlinear systems of equations -- Boundary-value problems for ordinary differential equations -- Numerical solutions to partial differential equations.…”
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Computational quantum chemistry an interactive guide to basis set theory / by Quinn, Charles M.

Table of Contents: “…Machine generated contents note: 1 Essential atomic orbital theory -- 11 Atomic orbitals for the hydrogen atom -- 12 Radial distribution functions for the hydrogen atom -- 13 Radial wave functions for many-electron atoms -- 14 Slater-type orbitals -- 15 Gaussian-type functions-the Isto-3g) minimal basis set -- 16 isto-ng) basis sets -- 17 Scaling factors -- 18 The (4s/2s) basis set, polarization and scaling factors for molecular -- environments -- 19 Gaussian-lobe and other Gaussian basis sets -- 2 Numerical integration -- 21 Numerical integration -- 22 Application of Simpson's rule to calculate a normalization integral -- 23 Calculations of normalization constants over the angular coordinates -- 24 Numerical integration in a cylindrical volume: diatomic and linear -- molecular geometries -- 25 Calculation of the overlap integral between Is orbitals in a Gaussian -- basis -- 26 Designing Gaussian basis sets to model Slater orbitals -- 3 Orthonormality -- 31 Orthonormality in Slater orbital and basis set theory -- 32 Orthonormality and Slater orbitals -- 33 Orthonormality and Gaussian orbitals -- 34 Orthonormality and double-zeta Slater orbitals -- 35 Orthonormality and split-basis or double-zeta Gaussian basis sets -- 36 The Jacobi transformation, diagonalization of a symmetric matrix and -- canonical orthogonalization -- 37 The S-1/2 'trick' -- 38 Symmetric orthonormalization -- 4 The hydrogen atom -numerical solutions -- 41 Eigenvalue calculations for hydrogen based on analytical functions -- 42 Calculations using Slater orbitals -- 43 Calculations with Gaussian functions -- 44 Calculations with split-basis [split-valence] sets -- 45 Review of results for the ls and 2s orbital energies in hydrogen -- 5 The helium atom and the self-consistent field -- 51 Hartree's analysis of the helium atom problem -- 52 Calculations with modified hydrogen atom wave functions -- 53 The Hall-Roothaan equations, the orbital approximation and -- the modem Hartree-Fock self-consistent field method -- 54 Calculations using Slater DZ functions -- 55 Gaussian basis set calculations for the helium atom-two-electron -- integrals over Gaussian basis functions -- 56 A HFS-SCF calculation with split-basis 14-31) for helium -- 57 Helium, singlet and triplet excited states, electron spin and the role -- of the Exchange integral -- 6 One- and two-electron diatoms -- 61 Calculations using hydrogen Is orbitals -- 62 Sto-3g calculations for H2+ -- 63 Calculations using Gaussian basis sets with the exact evaluation of -- integrals using Fourier transforms -- 64 Calculations involving the two-electron terms; the Isto-3g) -- HF-SCF results for dihydrogen -- 65 The standard form for the results of HFS-SCF calculations -- 66 The Isto-3g) HFS-SCF calculation for HeH+ -- 67 Polarization functions, Gaussian lobes and higher-order Gaussian -- basis sets -- 68 Epilogue.…”
An electronic book accessible through the World Wide Web; click to view

Computational quantum chemistry an interactive guide to basis set theory / by Quinn, Charles M.

Table of Contents: “…Machine generated contents note: 1 Essential atomic orbital theory -- 11 Atomic orbitals for the hydrogen atom -- 12 Radial distribution functions for the hydrogen atom -- 13 Radial wave functions for many-electron atoms -- 14 Slater-type orbitals -- 15 Gaussian-type functions-the Isto-3g) minimal basis set -- 16 isto-ng) basis sets -- 17 Scaling factors -- 18 The (4s/2s) basis set, polarization and scaling factors for molecular -- environments -- 19 Gaussian-lobe and other Gaussian basis sets -- 2 Numerical integration -- 21 Numerical integration -- 22 Application of Simpson's rule to calculate a normalization integral -- 23 Calculations of normalization constants over the angular coordinates -- 24 Numerical integration in a cylindrical volume: diatomic and linear -- molecular geometries -- 25 Calculation of the overlap integral between Is orbitals in a Gaussian -- basis -- 26 Designing Gaussian basis sets to model Slater orbitals -- 3 Orthonormality -- 31 Orthonormality in Slater orbital and basis set theory -- 32 Orthonormality and Slater orbitals -- 33 Orthonormality and Gaussian orbitals -- 34 Orthonormality and double-zeta Slater orbitals -- 35 Orthonormality and split-basis or double-zeta Gaussian basis sets -- 36 The Jacobi transformation, diagonalization of a symmetric matrix and -- canonical orthogonalization -- 37 The S-1/2 'trick' -- 38 Symmetric orthonormalization -- 4 The hydrogen atom -numerical solutions -- 41 Eigenvalue calculations for hydrogen based on analytical functions -- 42 Calculations using Slater orbitals -- 43 Calculations with Gaussian functions -- 44 Calculations with split-basis [split-valence] sets -- 45 Review of results for the ls and 2s orbital energies in hydrogen -- 5 The helium atom and the self-consistent field -- 51 Hartree's analysis of the helium atom problem -- 52 Calculations with modified hydrogen atom wave functions -- 53 The Hall-Roothaan equations, the orbital approximation and -- the modem Hartree-Fock self-consistent field method -- 54 Calculations using Slater DZ functions -- 55 Gaussian basis set calculations for the helium atom-two-electron -- integrals over Gaussian basis functions -- 56 A HFS-SCF calculation with split-basis 14-31) for helium -- 57 Helium, singlet and triplet excited states, electron spin and the role -- of the Exchange integral -- 6 One- and two-electron diatoms -- 61 Calculations using hydrogen Is orbitals -- 62 Sto-3g calculations for H2+ -- 63 Calculations using Gaussian basis sets with the exact evaluation of -- integrals using Fourier transforms -- 64 Calculations involving the two-electron terms; the Isto-3g) -- HF-SCF results for dihydrogen -- 65 The standard form for the results of HFS-SCF calculations -- 66 The Isto-3g) HFS-SCF calculation for HeH+ -- 67 Polarization functions, Gaussian lobes and higher-order Gaussian -- basis sets -- 68 Epilogue.…”
An electronic book accessible through the World Wide Web; click to view

Differential equations : first and second order linear differential equations / by Saha, Snehanshu

Table of Contents: “…-- 1.1.2 Solution to a differential equation -- 1.1.3 Family of solutions -- 1.1.4 Direction fields -- 1.2 Some linear algebra -- 1.2.1 Matrices -- 1.2.2 Systems of linear equations -- 1.2.3 Matrix addition and subtraction and scalar product -- 1.2.4 Transpose of a matrix -- 1.2.5 Dot product and matrix multiplication -- 1.2.6 Determinants -- 1.2.7 The inverse of a square matrix -- 1.2.8 Matrix form of a system of linear equations -- 1.2.9 Linear dependence -- 1.2.10 Eigenvalues and Eigenvectors -- 1.2.11 Diagonalization --…”
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Differential equations : first and second order linear differential equations / by Saha, Snehanshu

Table of Contents: “…-- 1.1.2 Solution to a differential equation -- 1.1.3 Family of solutions -- 1.1.4 Direction fields -- 1.2 Some linear algebra -- 1.2.1 Matrices -- 1.2.2 Systems of linear equations -- 1.2.3 Matrix addition and subtraction and scalar product -- 1.2.4 Transpose of a matrix -- 1.2.5 Dot product and matrix multiplication -- 1.2.6 Determinants -- 1.2.7 The inverse of a square matrix -- 1.2.8 Matrix form of a system of linear equations -- 1.2.9 Linear dependence -- 1.2.10 Eigenvalues and Eigenvectors -- 1.2.11 Diagonalization --…”
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Statistical monitoring of complex multivariate processes with applications in industrial process control / by Krüger, Uwe, Dr

Table of Contents: “…Machine generated contents note: Preface Introduction I Fundamentals of Multivariate Statistical Process Control 1 Motivation for Multivariate Statistical Process Control 1.1 Summary of Statistical Process Control 1.1.1 Roots and Evolution of Statistical Process Control 1.1.2 Principles of Statistical Process Control 1.1.3 Hypothesis Testing, Type I and II errors 1.2 Why Multivariate Statistical Process Control 1.2.1 Statistically Uncorrelated Variables 1.2.2 Perfectly Correlated Variables 1.2.3 Highly Correlated Variables 1.2.4 Type I and II Errors and Dimension Reduction 1.3 Tutorial Session 2 Multivariate Data Modeling Methods 2.1 Principal Component Analysis 2.1.1 Assumptions for Underlying Data Structure 2.1.2 Geometric Analysis of Data Structure 2.1.3 A Simulation Example 2.2 Partial Least Squares 2.2.1 Assumptions for Underlying Data Structure 2.2.2 Deflation Procedure for Estimating Data Models 2.2.3 A Simulation Example 2.3 Maximum Redundancy Partial Least Squares 2.3.1 Assumptions for Underlying Data Structure 2.3.2 Source Signal Estimation 2.3.3 Geometric Analysis of Data Structure 2.3.4 A Simulation Example 2.4 Estimating the Number of Source Signals 2.4.1 Stopping Rules for PCA Models 2.4.2 Stopping Rules for PLS Models 2.5 Tutorial Session 3 Process Monitoring Charts 3.1 Fault Detection 3.1.1 Scatter Diagrams 3.1.2 Nonnegative Quadratic Monitoring Statistics 3.2 Fault Isolation and Identification 3.2.1 Contribution Charts 3.2.2 Residual-Based Tests 3.2.3 Variable Reconstruction 3.3 Geometry of Variable Projections 3.3.1 Linear Dependency of Projection Residuals 3.3.2 Geometric Analysis of Variable Reconstruction 3.4 Tutorial Session II Application Studies 4 Application to a Chemical Reaction Process 4.1 Process Description 4.2 Identification of a Monitoring Model 4.3 Diagnosis of a Fault Condition 5 Application to a Distillation Process 5.1 Process Description 5.2 Identification of a Monitoring Model 5.3 Diagnosis of a Fault Condition III Advances in Multivariate Statistical Process Control 6 Further Modeling Issues 6.1 Accuracy of Estimating PCA Models 6.1.1 Revisiting the Eigendecomposition of Sz0z0 6.1.2 Two Illustrative Examples 6.1.3 Maximum Likelihood PCA for Known Sgg 6.1.4 Maximum Likelihood PCA for Unknown Sgg 6.1.5 A Simulation Example 6.1.6 A Stopping Rule for Maximum Likelihood PCA Models 6.1.7 Properties of Model and Residual Subspace Estimates 6.1.8 Application to a Chemical Reaction Process - Revisited 6.2 Accuracy of Estimating PLS Models 6.2.1 Bias and Variance of Parameter Estimation 6.2.2 Comparing Accuracy of PLS and OLS Regression Models 6.2.3 Impact of Error-in-Variables Structure upon PLS Models 6.2.4 Error-in-Variable Estimate for Known See 6.2.5 Error-in-Variable Estimate for Unknown See 6.2.6 Application to a Distillation Process - Revisited 6.3 Robust Model Estimation 6.3.1 Robust Parameter Estimation 6.3.2 Trimming Approaches 6.4 Small Sample Sets 6.5 Tutorial Session 7 Monitoring Multivariate Time-Varying Processes 7.1 Problem Analysis 7.2 Recursive Principal Component Analysis 7.3 MovingWindow Principal Component Analysis 7.3.1 Adapting the Data Correlation Matrix 7.3.2 Adapting the Eigendecomposition 7.3.3 Computational Analysis of the Adaptation Procedure 7.3.4 Adaptation of Control Limits 7.3.5 Process Monitoring using an Application Delay 7.3.6 MinimumWindow Length 7.4 A Simulation Example 7.4.1 Data Generation 7.4.2 Application of PCA 7.4.3 Utilizing MWPCA based on an Application Delay 7.5 Application to a Fluid Catalytic Cracking Unit 7.5.1 Process Description 7.5.2 Data Generation 7.5.3 Pre-analysis of Simulated Data 7.5.4 Application of PCA 7.5.5 Application of MWPCA 7.6 Application to a Furnace Process 7.6.1 Process Description 7.6.2 Description of Sensor Bias 7.6.3 Application of PCA 7.6.4 Utilizing MWPCA based on an Application Delay 7.7 Adaptive Partial Least Squares 7.7.1 Recursive Adaptation of Sx0x0 and Sx0y0 7.7.2 MovingWindow Adaptation of Sv0v0 and Sv0y0 7.7.3 Adapting The Number of Source Signals 7.7.4 Adaptation of the PLS Model 7.8 Tutorial Session 8 Monitoring Changes in Covariance Structure 8.1 Problem Analysis 8.1.1 First Intuitive Example 8.1.2 Generic Statistical Analysis 8.1.3 Second Intuitive Example 8.2 Preliminary Discussion of Related Techniques 8.3 Definition of Primary and Improved Residuals 8.3.1 Primary Residuals for Eigenvectors 8.3.2 Primary Residuals for Eigenvalues 8.3.3 Comparing both Types of Primary Residuals 8.3.4 Statistical Properties of Primary Residuals 8.3.5 Improved Residuals for Eigenvalues 8.4 Revisiting the Simulation Examples in Section 8.1 8.4.1 First Simulation Example 8.4.2 Second Simulation Example 8.5 Fault Isolation and Identification 8.5.1 Diagnosis of Step-Type Fault Conditions 8.5.2 Diagnosis of General Deterministic Fault Conditions 8.5.3 A Simulation Example 8.6 Application Study to a Gearbox System 8.6.1 Process Description 8.6.2 Fault Description 8.6.3 Identification of a Monitoring Model 8.6.4 Detecting a Fault Condition 8.7 Analysis of Primary and Improved Residuals 8.7.1 Central Limit Theorem 8.7.2 Further Statistical Properties of Primary Residuals 8.7.3 Sensitivity of Statistics based on Improved Residuals 8.8 Tutorial Session IV Description of Modeling Methods 9 Principal Component Analysis 9.1 The Core Algorithm 9.2 Summary of the PCA Algorithm 9.3 Properties of a PCA Model 10 Partial Least Squares 10.1 Preliminaries 10.2 The Core Algorithm 10.3 Summary of the PLS Algorithm10.4 Properties of PLS 10.5 Properties of Maximum Redundancy PLS References Index.…”
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