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Matrix calculus / / by E. Bodewig
| Matrix calculus / / by E. Bodewig |
| Autore | Bodewig Ewald |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Amsterdam, Netherlands : , : North-Holland Publishing Company, , 1959 |
| Descrizione fisica | 1 online resource (465 p.) |
| Disciplina | 512.896 |
| Soggetto topico | Matrices |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4832-7498-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Dedication; Matrix Calculus; CopyrightPage; Table of Contents; PREFACE; PART I: MATRIX CALCULUS; CHAPTER I. VECTORS; 1.1. EQUATION OF A PLANE; CHAPTER II. MATRICES; CHAPTER 3. FURTHER APPLICATIONS; CHAPTER 4. MEASURES OF THE MAGNITUDE OF A MATRIX; CHAPTER 5. FORMS; CHAPTER 6. EIGENVALUES; 6.1. MODAL-MATRIX, SPECTRAL-MATRIX; 6.2. THE CHARACTERISTIC EQUATION; 6.3. RELATIONS BETWEEN Sp, N, |A|,λi; 6.4. EIGENROWS; 6.5. EXTREMUM PROPERTIES OF THE EIGENVALUES; 6.6. BOUNDS FOR THE EIGENVALUES; 6.7. BOUNDS FOR THE DETERMINANT; 6.8. ELEMENTARY DIVISORS; PART II: LINEAR EQUATIONS
A. DIRECT METHODSCHAPTER 1. EXACT SOLUTIONS; 1.1. ELIMINATION I; 1.2. ELIMINATION II; CHAPTER 2. APPROXIMATE SOLUTIONS; 2.1. CONDENSATION I. TRIANGULARISATION; 2.2. CONDENSATION II. DIAGONALIZATION; 2 . 3 . THE DECOMPOSITION OF THE MATRIX INTO TWO TRIANGULAR MATRICES; 2.4. CHOICE OF ANOTHER PIVOTAL ELEMENT; 2.5. THE GAUSS-DOOLITTLE PROCESS; 2.6. A METHOD FOR PUNCHED CARDS; 2.7. THE GENERALIZED CONDENSATIONS I AND II; 2.8. AlTKENS TRIPLE PRODUCT; 2.9. ILL-CONDITIONED EQUATIONS; 2.10. NEIGHBOUR SYSTEMS; 2.11. ERRORS AND EXACTNESS OF THE SOLUTION; 2.12. COMPLEX SYSTEMS; B. ITERATIONS METHODS CHAPTER 3.3.1. INTRODUCTION; 3.2. PRELIMINARY VIEW; 3.3. DEVELOPMENT OF THE ITERATION METHODS; CHAPTER 4. ITERATION I; CHAPTER 5. THE CHARACTERISTIC EQUATION OF THE ITERATION PROCESSES; CHAPTER 6. TYPE OF CONVERGENCE OF THE ITERATION METHODS; CHAPTER 7. CONVERGENCE THEOREMS; 7.1. SCHMIDT-MISES-GEIRINGER; 7.3. ITERATION II; 7.4. ITERATION I; 7.5. GEIRINGER'S THEOREM; 7.6. THEOREM OF STEIN AND ROSENBERG; 7.7. ANOTHER THEOREM OF STEIN-ROSENBERG; 7.8. AITKEN'S NEO-SEIDELIAN ITERATION; CHAPTER 8. THE GENERAL ITERATION; CHAPTER 9. METHODS FOR AUTOMATIC MACHINES CHAPTER 10. SPEEDING - U P CONVERGENCE BY CHANGING MATRIX10.1. CESARl'S METHOD; 10.2. VAN DER CORPUT'S DEVICE; 10.3. THE METHOD OF ELIMINATION; 10.4. JACOBl'S METHOD; CHAPTER 11. THE ITERATED DIRECT METHODS; 11.1. CONVERGENCE OF THE METHOD; CHAPTER 12. METHODS FOR ELECTRONIC COMPUTERS; 12.1. KACMARZ'S PROCEDURE; 12.2. CIMMINO'S PROCEDURE; 12.3. LINEAR EQUATIONS AS MINIMUM CONDITION; 12.4. LINEAR EQUATIONS AS EIGENPROBLEMS; CHAPTER 13. VARIOUS QUESTIONS; 13.1. NORMALIZATION; 13.2. SCALING; 13.3. ANOTHER SCALING; 13.4. A THIRD SCALING; PART IIII: NVERSION OF MATRICES; A. DIRECT METHODS CHAPTER 1. CONDENSATION1.1. THE INVERSE OF A TRIANGULAR MATRIX; CHAPTER 2. FROBENIUS-SCHUR'S RELATION; CHAPTER 3. COMPLETING; CHAPTER 4. THE ADJUGATE; 4 . 1 . THE METHOD OF DETERMINANTS; B. ITERATION METHOD; C. GEODETIC MATRICES; PART IV. EIGEN PROBLEMS; CHAPTER 1. INTRODUCTORY; A. ITERATION METHODS; CHAPTER 2. THE ITERATED VECTORS {Power Method); 2.1. THE DOMINANT EIGENVALUE IS REAL; 2.2. THE DOMINANT EIGENVALUE IS COMPLEX; 2.3. OTHER CASES; 2.4. CRITICISM OF THE POWER METHOD; 2.5. HIGHER EIGENVALUES; 2.6. HIGHER EIGENVALUES ACCORDING TO AITKEN; 2.7. THE LEAST EIGENVALUES 2.8. THE USE OF FROBENIUS'S THEOREM |
| Record Nr. | UNINA-9910480098903321 |
Bodewig Ewald
|
||
| Amsterdam, Netherlands : , : North-Holland Publishing Company, , 1959 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Matrix calculus / / E. Bodewig
| Matrix calculus / / E. Bodewig |
| Autore | Bodewig Ewald |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Amsterdam : , : North-Holland Publishing Company, , 1959 |
| Descrizione fisica | 1 online resource (465 pages) : illustrations |
| Disciplina | 512.896 |
| Soggetto topico | Matrices |
| ISBN | 1-4832-7498-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Dedication; Matrix Calculus; CopyrightPage; Table of Contents; PREFACE; PART I: MATRIX CALCULUS; CHAPTER I. VECTORS; 1.1. EQUATION OF A PLANE; CHAPTER II. MATRICES; CHAPTER 3. FURTHER APPLICATIONS; CHAPTER 4. MEASURES OF THE MAGNITUDE OF A MATRIX; CHAPTER 5. FORMS; CHAPTER 6. EIGENVALUES; 6.1. MODAL-MATRIX, SPECTRAL-MATRIX; 6.2. THE CHARACTERISTIC EQUATION; 6.3. RELATIONS BETWEEN Sp, N, |A|,λi; 6.4. EIGENROWS; 6.5. EXTREMUM PROPERTIES OF THE EIGENVALUES; 6.6. BOUNDS FOR THE EIGENVALUES; 6.7. BOUNDS FOR THE DETERMINANT; 6.8. ELEMENTARY DIVISORS; PART II: LINEAR EQUATIONS
A. DIRECT METHODS; CHAPTER 1. EXACT SOLUTIONS; 1.1. ELIMINATION I; 1.2. ELIMINATION II; CHAPTER 2. APPROXIMATE SOLUTIONS; 2.1. CONDENSATION I. TRIANGULARISATION; 2.2. CONDENSATION II. DIAGONALIZATION; 2 . 3 . THE DECOMPOSITION OF THE MATRIX INTO TWO TRIANGULAR MATRICES; 2.4. CHOICE OF ANOTHER PIVOTAL ELEMENT; 2.5. THE GAUSS-DOOLITTLE PROCESS; 2.6. A METHOD FOR PUNCHED CARDS; 2.7. THE GENERALIZED CONDENSATIONS I AND II; 2.8. AlTKENS TRIPLE PRODUCT; 2.9. ILL-CONDITIONED EQUATIONS; 2.10. NEIGHBOUR SYSTEMS; 2.11. ERRORS AND EXACTNESS OF THE SOLUTION; 2.12. COMPLEX SYSTEMS; B. ITERATIONS METHODS CHAPTER 3.3.1. INTRODUCTION; 3.2. PRELIMINARY VIEW; 3.3. DEVELOPMENT OF THE ITERATION METHODS; CHAPTER 4. ITERATION I; CHAPTER 5. THE CHARACTERISTIC EQUATION OF THE ITERATION PROCESSES; CHAPTER 6. TYPE OF CONVERGENCE OF THE ITERATION METHODS; CHAPTER 7. CONVERGENCE THEOREMS; 7.1. SCHMIDT-MISES-GEIRINGER; 7.3. ITERATION II; 7.4. ITERATION I; 7.5. GEIRINGER'S THEOREM; 7.6. THEOREM OF STEIN AND ROSENBERG; 7.7. ANOTHER THEOREM OF STEIN-ROSENBERG; 7.8. AITKEN'S NEO-SEIDELIAN ITERATION; CHAPTER 8. THE GENERAL ITERATION; CHAPTER 9. METHODS FOR AUTOMATIC MACHINES CHAPTER 10. SPEEDING - U P CONVERGENCE BY CHANGING MATRIX; 10.1. CESARl'S METHOD; 10.2. VAN DER CORPUT'S DEVICE; 10.3. THE METHOD OF ELIMINATION; 10.4. JACOBl'S METHOD; CHAPTER 11. THE ITERATED DIRECT METHODS; 11.1. CONVERGENCE OF THE METHOD; CHAPTER 12. METHODS FOR ELECTRONIC COMPUTERS; 12.1. KACMARZ'S PROCEDURE; 12.2. CIMMINO'S PROCEDURE; 12.3. LINEAR EQUATIONS AS MINIMUM CONDITION; 12.4. LINEAR EQUATIONS AS EIGENPROBLEMS; CHAPTER 13. VARIOUS QUESTIONS; 13.1. NORMALIZATION; 13.2. SCALING; 13.3. ANOTHER SCALING; 13.4. A THIRD SCALING; PART IIII: NVERSION OF MATRICES; A. DIRECT METHODS CHAPTER 1. CONDENSATION; 1.1. THE INVERSE OF A TRIANGULAR MATRIX; CHAPTER 2. FROBENIUS-SCHUR'S RELATION; CHAPTER 3. COMPLETING; CHAPTER 4. THE ADJUGATE; 4 . 1 . THE METHOD OF DETERMINANTS; B. ITERATION METHOD; C. GEODETIC MATRICES; PART IV. EIGEN PROBLEMS; CHAPTER 1. INTRODUCTORY; A. ITERATION METHODS; CHAPTER 2. THE ITERATED VECTORS {Power Method); 2.1. THE DOMINANT EIGENVALUE IS REAL; 2.2. THE DOMINANT EIGENVALUE IS COMPLEX; 2.3. OTHER CASES; 2.4. CRITICISM OF THE POWER METHOD; 2.5. HIGHER EIGENVALUES; 2.6. HIGHER EIGENVALUES ACCORDING TO AITKEN; 2.7. THE LEAST EIGENVALUES; 2.8. THE USE OF FROBENIUS'S THEOREM |
| Record Nr. | UNINA-9910786794903321 |
|
Bodewig Ewald
|
||
| Amsterdam : , : North-Holland Publishing Company, , 1959 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Matrix calculus / / E. Bodewig
| Matrix calculus / / E. Bodewig |
| Autore | Bodewig Ewald |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Amsterdam : , : North-Holland Publishing Company, , 1959 |
| Descrizione fisica | 1 online resource (465 pages) : illustrations |
| Disciplina | 512.896 |
| Soggetto topico | Matrices |
| ISBN | 1-4832-7498-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Dedication; Matrix Calculus; CopyrightPage; Table of Contents; PREFACE; PART I: MATRIX CALCULUS; CHAPTER I. VECTORS; 1.1. EQUATION OF A PLANE; CHAPTER II. MATRICES; CHAPTER 3. FURTHER APPLICATIONS; CHAPTER 4. MEASURES OF THE MAGNITUDE OF A MATRIX; CHAPTER 5. FORMS; CHAPTER 6. EIGENVALUES; 6.1. MODAL-MATRIX, SPECTRAL-MATRIX; 6.2. THE CHARACTERISTIC EQUATION; 6.3. RELATIONS BETWEEN Sp, N, |A|,λi; 6.4. EIGENROWS; 6.5. EXTREMUM PROPERTIES OF THE EIGENVALUES; 6.6. BOUNDS FOR THE EIGENVALUES; 6.7. BOUNDS FOR THE DETERMINANT; 6.8. ELEMENTARY DIVISORS; PART II: LINEAR EQUATIONS
A. DIRECT METHODS; CHAPTER 1. EXACT SOLUTIONS; 1.1. ELIMINATION I; 1.2. ELIMINATION II; CHAPTER 2. APPROXIMATE SOLUTIONS; 2.1. CONDENSATION I. TRIANGULARISATION; 2.2. CONDENSATION II. DIAGONALIZATION; 2 . 3 . THE DECOMPOSITION OF THE MATRIX INTO TWO TRIANGULAR MATRICES; 2.4. CHOICE OF ANOTHER PIVOTAL ELEMENT; 2.5. THE GAUSS-DOOLITTLE PROCESS; 2.6. A METHOD FOR PUNCHED CARDS; 2.7. THE GENERALIZED CONDENSATIONS I AND II; 2.8. AlTKENS TRIPLE PRODUCT; 2.9. ILL-CONDITIONED EQUATIONS; 2.10. NEIGHBOUR SYSTEMS; 2.11. ERRORS AND EXACTNESS OF THE SOLUTION; 2.12. COMPLEX SYSTEMS; B. ITERATIONS METHODS CHAPTER 3.3.1. INTRODUCTION; 3.2. PRELIMINARY VIEW; 3.3. DEVELOPMENT OF THE ITERATION METHODS; CHAPTER 4. ITERATION I; CHAPTER 5. THE CHARACTERISTIC EQUATION OF THE ITERATION PROCESSES; CHAPTER 6. TYPE OF CONVERGENCE OF THE ITERATION METHODS; CHAPTER 7. CONVERGENCE THEOREMS; 7.1. SCHMIDT-MISES-GEIRINGER; 7.3. ITERATION II; 7.4. ITERATION I; 7.5. GEIRINGER'S THEOREM; 7.6. THEOREM OF STEIN AND ROSENBERG; 7.7. ANOTHER THEOREM OF STEIN-ROSENBERG; 7.8. AITKEN'S NEO-SEIDELIAN ITERATION; CHAPTER 8. THE GENERAL ITERATION; CHAPTER 9. METHODS FOR AUTOMATIC MACHINES CHAPTER 10. SPEEDING - U P CONVERGENCE BY CHANGING MATRIX; 10.1. CESARl'S METHOD; 10.2. VAN DER CORPUT'S DEVICE; 10.3. THE METHOD OF ELIMINATION; 10.4. JACOBl'S METHOD; CHAPTER 11. THE ITERATED DIRECT METHODS; 11.1. CONVERGENCE OF THE METHOD; CHAPTER 12. METHODS FOR ELECTRONIC COMPUTERS; 12.1. KACMARZ'S PROCEDURE; 12.2. CIMMINO'S PROCEDURE; 12.3. LINEAR EQUATIONS AS MINIMUM CONDITION; 12.4. LINEAR EQUATIONS AS EIGENPROBLEMS; CHAPTER 13. VARIOUS QUESTIONS; 13.1. NORMALIZATION; 13.2. SCALING; 13.3. ANOTHER SCALING; 13.4. A THIRD SCALING; PART IIII: NVERSION OF MATRICES; A. DIRECT METHODS CHAPTER 1. CONDENSATION; 1.1. THE INVERSE OF A TRIANGULAR MATRIX; CHAPTER 2. FROBENIUS-SCHUR'S RELATION; CHAPTER 3. COMPLETING; CHAPTER 4. THE ADJUGATE; 4 . 1 . THE METHOD OF DETERMINANTS; B. ITERATION METHOD; C. GEODETIC MATRICES; PART IV. EIGEN PROBLEMS; CHAPTER 1. INTRODUCTORY; A. ITERATION METHODS; CHAPTER 2. THE ITERATED VECTORS {Power Method); 2.1. THE DOMINANT EIGENVALUE IS REAL; 2.2. THE DOMINANT EIGENVALUE IS COMPLEX; 2.3. OTHER CASES; 2.4. CRITICISM OF THE POWER METHOD; 2.5. HIGHER EIGENVALUES; 2.6. HIGHER EIGENVALUES ACCORDING TO AITKEN; 2.7. THE LEAST EIGENVALUES; 2.8. THE USE OF FROBENIUS'S THEOREM |
| Record Nr. | UNINA-9910827884803321 |
|
Bodewig Ewald
|
||
| Amsterdam : , : North-Holland Publishing Company, , 1959 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||