Matrix calculus /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bodewig, Ewald (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam, Netherlands : North-Holland Publishing Company, 1959.
Temas:
Matrices.
Matrices
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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, [lambda]i; 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 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.
  • 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.

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