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Formulas useful for linear regression analysis and related matrix theory : it's only formulas but we like them / / Simo Puntanen, George P.H. Styan, Jarkko Isotalo
| Formulas useful for linear regression analysis and related matrix theory : it's only formulas but we like them / / Simo Puntanen, George P.H. Styan, Jarkko Isotalo |
| Autore | Puntanen Simo |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (137 p.) |
| Disciplina | 510.212 |
| Altri autori (Persone) |
StyanGeorge Peter Hansbenno
IsotaloJarkko |
| Collana | Springer briefs in statistics |
| Soggetto topico |
Linear systems - Mathematical models
Mathematics - Formulae |
| ISBN | 3-642-32931-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The Model Matrix -- Fitted Values and Residuals -- Regression Coefficients -- Alternative Estimators -- Decompositions of Sums of Squares -- Partial Correlations -- Distributions -- Testing Hypotheses -- Diagnostics -- BLUE: Some Helpful Identities -- Estimability -- Best Linear Unbiased Estimator -- The Watson Efficiency -- Linear Sufficiency and Admissibility -- Best Linear Unbiased Predictor -- Mixed Model -- Multivariate Linear Model -- Inverse of a Partitioned Matrix -- Generalized Inverses -- Projectors -- Eigenvalues -- Discriminant Analysis -- Factor Analysis -- Canonical Correlations -- Matrix Decompositions -- Principal Component Analysis -- Löwner Ordering -- Rank Rules -- Inequalities -- Kronecker Product -- Matrix Derivatives. |
| Record Nr. | UNINA-9910438151603321 |
Puntanen Simo
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| New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Introduction to mathematical systems theory : discrete time linear systems, control and identification / / Christiaan Heij, AndreÌ C. M. Ran, Frederik van Schagen
| Introduction to mathematical systems theory : discrete time linear systems, control and identification / / Christiaan Heij, AndreÌ C. M. Ran, Frederik van Schagen |
| Autore | Heij C. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (199 pages) |
| Disciplina | 003 |
| Soggetto topico |
Linear systems - Mathematical models
Discrete-time systems - Mathematical models |
| ISBN | 3-030-59654-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466550703316 |
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Heij C.
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Introduction to mathematical systems theory : discrete time linear systems, control and identification / / Christiaan Heij, AndreÌ C. M. Ran, Frederik van Schagen
| Introduction to mathematical systems theory : discrete time linear systems, control and identification / / Christiaan Heij, AndreÌ C. M. Ran, Frederik van Schagen |
| Autore | Heij C. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (199 pages) |
| Disciplina | 003 |
| Soggetto topico |
Linear systems - Mathematical models
Discrete-time systems - Mathematical models |
| ISBN | 3-030-59654-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910484927803321 |
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Heij C.
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The nth-order comprehensive adjoint sensitivity analysis methodology . Volume 1 : overcoming the curse of dimensionality : linear systems / / Dan Gabriel Cacuci
| The nth-order comprehensive adjoint sensitivity analysis methodology . Volume 1 : overcoming the curse of dimensionality : linear systems / / Dan Gabriel Cacuci |
| Autore | Cacuci Dan Gabriel |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (373 pages) |
| Disciplina | 629.8312 |
| Soggetto topico |
Sensitivity theory (Mathematics)
Linear systems - Mathematical models |
| ISBN |
9783030963644
9783030963637 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Chapter 1: Motivation: Overcoming the Curse of Dimensionality in Sensitivity Analysis, Uncertainty Quantification, and Predict... -- 1.1 Introduction -- 1.2 Need for Computation of High-Order Response Sensitivities: An Illustrative Example -- 1.2.1 Sensitivity Analysis -- 1.2.2 Uncertainty Quantification: Moments of the Response Distribution -- 1.3 The Curse of Dimensionality in Sensitivity Analysis: Computation of High-Order Response Sensitivities to Model Parameters -- 1.4 The Curse of Dimensionality in Uncertainty Quantification: Moments of the Response Distribution in Parameter Phase-Space -- 1.4.1 Expectation Value of a Response -- 1.4.2 Response-Parameter Covariances -- 1.4.3 Covariance of Two Responses -- 1.4.4 Triple Correlations Among Responses and Parameters -- 1.4.5 Quadruple Correlations Among Responses and Parameters -- 1.5 Chapter Summary -- Chapter 2: The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Sy... -- 2.1 Introduction -- 2.2 Mathematical Modeling of Response-Coupled Linear Forward and Adjoint Systems -- 2.3 The First-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (1s... -- 2.4 The Second-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (2... -- 2.5 The Third-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (3r... -- 2.6 The Fourth-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (4... -- 2.7 The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (... -- 2.7.1 The Pattern Underlying the nth-CASAM-L for n = 1, 2, 3, 4.
2.7.2 The Pattern Underlying the nth-CASAM-L: Arbitrarily High-Order n -- 2.7.3 Proving That the Framework for the nth-CASAM-L also Holds for the (n + 1)th-CASAM-L -- 2.8 The Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Coupled Forward/Adjoint Linear Systems (5th-CAS... -- 2.9 Chapter Summary -- Chapter 3: Illustrative Applications of the nth-CASAM-L to Paradigm Physical Systems with Imprecisely Known Properties, Intern... -- 3.1 Introduction -- 3.2 Transmission of Particles Through Media -- 3.2.1 Point-Detector Response -- 3.2.2 Particle Leakage Response -- 3.2.3 Reaction Rate Response -- 3.2.4 Contribution-Response Flux -- 3.3 Application of the 1st-CASAM-L to Compute First-Order Response Sensitivities to Imprecisely Known Parameters -- 3.3.1 Point-Detector Response -- 3.3.2 Particle Leakage Response -- 3.3.3 Reaction Rate Response -- 3.3.4 Contribution-Response -- 3.4 Application of the 2nd-CASAM-L to Compute Second-Order Response Sensitivities to Imprecisely Known Parameters -- 3.4.1 Determination of the Second-Order Sensitivities of the Form 2ρ(φ,ψ -- α)/αiμ(α), i = 1, , TP -- 3.4.2 Determination of the Second-Order Sensitivities of the Form 2ρ(φ,ψ -- α)/αib2, i = 1, , TP -- 3.4.3 Summary of Main Features Underlying the Computation of the Second-Order Sensitivities 2ρ(φ,ψ -- α)/αiαj, i, j = 1, , TP -- 3.5 Application of the 3rd-CASAM-L to Compute Third-Order Response Sensitivities to Imprecisely Known Parameters -- 3.5.1 Determination of the Third-Order Sensitivities of the Form 3ρ(φ,ψ -- α)/αiμ(α)μ(α), i = 1, , TP -- 3.5.2 Determination of the Third-Order Sensitivities of the Form 3ρ(φ,ψ -- α)/αib1b2, i = 1, , TP -- 3.6 Illustrative Application of the 4th-CASAM-L to a Paradigm Time-Evolution Model. 3.6.1 Applying the 1st-CASAM-L to Compute the first-Order Sensitivities to Model Parameters, Including Imprecisely Known Initi... -- 3.6.2 Applying the 2nd-CASAM-L to Compute the Second-Order Response Sensitivities to Model Parameters, Including Imprecisely K... -- 3.6.2.1 Second-Order Sensitivities Corresponding to R1(ρ -- α)/σi, i = 1, , N -- 3.6.2.2 Second-Order Sensitivities Corresponding to R1(ρ -- α)/ni, i = 1, , N -- 3.6.2.3 Second-Order Sensitivities Corresponding to R1(ρ -- α)/ρin -- 3.6.2.4 Second-Order Sensitivities Corresponding to R1(ρ -- α)/td -- 3.6.2.5 Second-Order Sensitivities Corresponding to R1(ρ -- α)/β -- 3.6.2.6 Independent Mutual Verification of Adjoint Sensitivity Functions -- 3.6.2.7 Aggregating Model Parameters to Reduce the Number of Large-Scale Adjoint Computations for Determining the Second-Order... -- 3.6.2.8 Illustrative Computation of Third- and Fourth-Order Sensitivities Using Aggregated Model Parameters -- 3.6.3 Applying the nth-CASAM-L to Compute Sensitivities of the Average Concentration Response to Model Parameters, Including I... -- 3.6.3.1 First-Order Sensitivities -- 3.6.3.2 Second-Order Sensitivities -- 3.7 Chapter Summary -- Chapter 4: Sensitivity Analysis of Neutron Transport Modeled by the Forward and Adjoint Linear Boltzmann Equations -- 4.1 Introduction -- 4.2 Paradigm Physical System: Neutron Transport in a Multiplying Medium with Source -- 4.3 Application of the 1st-CASAM-L to Determine the First-Order Sensitivities of R(φ,φ+ -- α) -- 4.4 Application of the 2nd-CASAM-L to Determine the Second-Order Sensitivities of R(φ,φ+ -- α) -- 4.4.1 Determination of the Second-Order Sensitivities of the Form -- 4.4.2 Determination of the Second-Order Sensitivities of the Form -- 4.4.3 Determination of the Second-Order Sensitivities of the Form -- 4.4.4 Determination of the Second-Order Sensitivities of the Form. 4.4.5 Determination of the Second-Order Sensitivities of the Form -- 4.4.6 Determination of the Second-Order Sensitivities of the Form -- 4.4.7 Determination of the Second-Order Sensitivities of the Form -- 4.5 Second-Order Sensitivity Analysis of the Schwinger and Roussopoulos Functionals -- 4.5.1 Application of the 1st-CASAM-L to Determine the First-Order Sensitivities of the Roussopoulos and Schwinger Functionals ... -- 4.5.2 Application of the 2nd-CASAM-L to Determine the Second-Order Sensitivities of the Schwinger and Roussopoulos Functionals... -- 4.5.2.1 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.2 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.3 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.4 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.5 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.6 Determination of the Second-Order Sensitivities of the Form -- 4.6 Chapter Summary -- Chapter 5: Concluding Remarks -- References -- Index. |
| Record Nr. | UNINA-9910585793103321 |
|
Cacuci Dan Gabriel
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||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The nth-order comprehensive adjoint sensitivity analysis methodology . Volume 1 : overcoming the curse of dimensionality : linear systems / / Dan Gabriel Cacuci
| The nth-order comprehensive adjoint sensitivity analysis methodology . Volume 1 : overcoming the curse of dimensionality : linear systems / / Dan Gabriel Cacuci |
| Autore | Cacuci Dan Gabriel |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (373 pages) |
| Disciplina | 629.8312 |
| Soggetto topico |
Sensitivity theory (Mathematics)
Linear systems - Mathematical models |
| ISBN |
9783030963644
9783030963637 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Chapter 1: Motivation: Overcoming the Curse of Dimensionality in Sensitivity Analysis, Uncertainty Quantification, and Predict... -- 1.1 Introduction -- 1.2 Need for Computation of High-Order Response Sensitivities: An Illustrative Example -- 1.2.1 Sensitivity Analysis -- 1.2.2 Uncertainty Quantification: Moments of the Response Distribution -- 1.3 The Curse of Dimensionality in Sensitivity Analysis: Computation of High-Order Response Sensitivities to Model Parameters -- 1.4 The Curse of Dimensionality in Uncertainty Quantification: Moments of the Response Distribution in Parameter Phase-Space -- 1.4.1 Expectation Value of a Response -- 1.4.2 Response-Parameter Covariances -- 1.4.3 Covariance of Two Responses -- 1.4.4 Triple Correlations Among Responses and Parameters -- 1.4.5 Quadruple Correlations Among Responses and Parameters -- 1.5 Chapter Summary -- Chapter 2: The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Sy... -- 2.1 Introduction -- 2.2 Mathematical Modeling of Response-Coupled Linear Forward and Adjoint Systems -- 2.3 The First-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (1s... -- 2.4 The Second-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (2... -- 2.5 The Third-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (3r... -- 2.6 The Fourth-Order Comprehensive Sensitivity Analysis Methodology for Response-Coupled Linear Forward and Adjoint Systems (4... -- 2.7 The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (... -- 2.7.1 The Pattern Underlying the nth-CASAM-L for n = 1, 2, 3, 4.
2.7.2 The Pattern Underlying the nth-CASAM-L: Arbitrarily High-Order n -- 2.7.3 Proving That the Framework for the nth-CASAM-L also Holds for the (n + 1)th-CASAM-L -- 2.8 The Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Coupled Forward/Adjoint Linear Systems (5th-CAS... -- 2.9 Chapter Summary -- Chapter 3: Illustrative Applications of the nth-CASAM-L to Paradigm Physical Systems with Imprecisely Known Properties, Intern... -- 3.1 Introduction -- 3.2 Transmission of Particles Through Media -- 3.2.1 Point-Detector Response -- 3.2.2 Particle Leakage Response -- 3.2.3 Reaction Rate Response -- 3.2.4 Contribution-Response Flux -- 3.3 Application of the 1st-CASAM-L to Compute First-Order Response Sensitivities to Imprecisely Known Parameters -- 3.3.1 Point-Detector Response -- 3.3.2 Particle Leakage Response -- 3.3.3 Reaction Rate Response -- 3.3.4 Contribution-Response -- 3.4 Application of the 2nd-CASAM-L to Compute Second-Order Response Sensitivities to Imprecisely Known Parameters -- 3.4.1 Determination of the Second-Order Sensitivities of the Form 2ρ(φ,ψ -- α)/αiμ(α), i = 1, , TP -- 3.4.2 Determination of the Second-Order Sensitivities of the Form 2ρ(φ,ψ -- α)/αib2, i = 1, , TP -- 3.4.3 Summary of Main Features Underlying the Computation of the Second-Order Sensitivities 2ρ(φ,ψ -- α)/αiαj, i, j = 1, , TP -- 3.5 Application of the 3rd-CASAM-L to Compute Third-Order Response Sensitivities to Imprecisely Known Parameters -- 3.5.1 Determination of the Third-Order Sensitivities of the Form 3ρ(φ,ψ -- α)/αiμ(α)μ(α), i = 1, , TP -- 3.5.2 Determination of the Third-Order Sensitivities of the Form 3ρ(φ,ψ -- α)/αib1b2, i = 1, , TP -- 3.6 Illustrative Application of the 4th-CASAM-L to a Paradigm Time-Evolution Model. 3.6.1 Applying the 1st-CASAM-L to Compute the first-Order Sensitivities to Model Parameters, Including Imprecisely Known Initi... -- 3.6.2 Applying the 2nd-CASAM-L to Compute the Second-Order Response Sensitivities to Model Parameters, Including Imprecisely K... -- 3.6.2.1 Second-Order Sensitivities Corresponding to R1(ρ -- α)/σi, i = 1, , N -- 3.6.2.2 Second-Order Sensitivities Corresponding to R1(ρ -- α)/ni, i = 1, , N -- 3.6.2.3 Second-Order Sensitivities Corresponding to R1(ρ -- α)/ρin -- 3.6.2.4 Second-Order Sensitivities Corresponding to R1(ρ -- α)/td -- 3.6.2.5 Second-Order Sensitivities Corresponding to R1(ρ -- α)/β -- 3.6.2.6 Independent Mutual Verification of Adjoint Sensitivity Functions -- 3.6.2.7 Aggregating Model Parameters to Reduce the Number of Large-Scale Adjoint Computations for Determining the Second-Order... -- 3.6.2.8 Illustrative Computation of Third- and Fourth-Order Sensitivities Using Aggregated Model Parameters -- 3.6.3 Applying the nth-CASAM-L to Compute Sensitivities of the Average Concentration Response to Model Parameters, Including I... -- 3.6.3.1 First-Order Sensitivities -- 3.6.3.2 Second-Order Sensitivities -- 3.7 Chapter Summary -- Chapter 4: Sensitivity Analysis of Neutron Transport Modeled by the Forward and Adjoint Linear Boltzmann Equations -- 4.1 Introduction -- 4.2 Paradigm Physical System: Neutron Transport in a Multiplying Medium with Source -- 4.3 Application of the 1st-CASAM-L to Determine the First-Order Sensitivities of R(φ,φ+ -- α) -- 4.4 Application of the 2nd-CASAM-L to Determine the Second-Order Sensitivities of R(φ,φ+ -- α) -- 4.4.1 Determination of the Second-Order Sensitivities of the Form -- 4.4.2 Determination of the Second-Order Sensitivities of the Form -- 4.4.3 Determination of the Second-Order Sensitivities of the Form -- 4.4.4 Determination of the Second-Order Sensitivities of the Form. 4.4.5 Determination of the Second-Order Sensitivities of the Form -- 4.4.6 Determination of the Second-Order Sensitivities of the Form -- 4.4.7 Determination of the Second-Order Sensitivities of the Form -- 4.5 Second-Order Sensitivity Analysis of the Schwinger and Roussopoulos Functionals -- 4.5.1 Application of the 1st-CASAM-L to Determine the First-Order Sensitivities of the Roussopoulos and Schwinger Functionals ... -- 4.5.2 Application of the 2nd-CASAM-L to Determine the Second-Order Sensitivities of the Schwinger and Roussopoulos Functionals... -- 4.5.2.1 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.2 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.3 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.4 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.5 Determination of the Second-Order Sensitivities of the Form -- 4.5.2.6 Determination of the Second-Order Sensitivities of the Form -- 4.6 Chapter Summary -- Chapter 5: Concluding Remarks -- References -- Index. |
| Record Nr. | UNISA-996483071503316 |
|
Cacuci Dan Gabriel
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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