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Introduction to precise numerical methods [[electronic resource] /] / Oliver Aberth
| Introduction to precise numerical methods [[electronic resource] /] / Oliver Aberth |
| Autore | Aberth Oliver |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Academic Press, c2007 |
| Descrizione fisica | 1 online resource (267 p.) |
| Disciplina | 518.0285 |
| Soggetto topico |
Computer science - Mathematics
Numerical analysis - Data processing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-96233-X
9786610962334 0-08-047120-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; 1 Introduction; 1.1 Open-source software; 1.2 Calling up a program; 1.3 Log files and print files; 1.4 More on log files; 1.5 The tilde notation for printed answers; 2 Computer Arithmetics; 2.1 Floating-point arithmetic; 2.2 Variable precision floating-point arithmetic; 2.3 Interval arithmetic; 2.4 Range arithmetic; 2.5 Practical range arithmetic; 2.6 Interval arithmetic notation; 2.7 Computing standard functions in range arithmetic; 2.8 Rational arithmetic; Software Exercises A; Notes and References; 3 Classification of Numerical Computation Problems; 3.1 A knotty problem
3.2 The impossibility of untying the knot 3.3 Repercussions from nonsolvable problem 3.1; 3.4 Some solvable and nonsolvable decimal place problems; 3.5 The solvable problems handled by calc; 3.6 Another nonsolvable problem; 3.7 The trouble with discontinuous functions; Notes and References; 4 Real-Valued Functions; 4.1 Elementary functions; Software Exercises B; 5 Computing Derivatives; 5.1 Power series of elementary functions; 5.2 An example of series evaluation; 5.3 Power series for elementary functions of several variables; 5.4 A more general method of generating power series 5.5 The demo program derivSoftware Exercises C; Notes and References; 6 Computing Integrals; 6.1 Computing a definite integral; 6.2 Formal interval arithmetic; 6.3 The demo program integ for computing ordinary definite integrals; 6.4 Taylor's remainder formula generalized; 6.5 The demo program mulint for higher dimensional integrals; 6.6 The demo program imprint for computing improper integrals; Software Exercises D; Notes and References; 7 Finding Where a Function f(x) is Zero; 7.1 Obtaining a solvable problem; 7.2 Using interval arithmetic for the problem; 7.3 Newton's method 7.4 Order of convergence Software Exercises E; 8 Finding Roots of Polynomials; 8.1 Polynomials; 8.2 A bound for the roots of a polynomial; 8.3 The Bairstow method for finding roots of a real polynomial; 8.4 Bounding the error of a rational polynomial's root approximations; 8.5 Finding accurate roots for a rational or a real polynomial; 8.6 The demo program roots; Software Exercises F; Notes and References; 9 Solving n Linear Equations in n Unknowns; 9.1 Notation; 9.2 Computation problems; 9.3 A method for solving linear equations; 9.4 Computing determinants 9.5 Finding the inverse of a square matrix 9.6 The demo programs equat, r_equat, and c_equat; Software Exercises G; Notes and References; 10 Eigenvalue and Eigenvector Problems; 10.1 Finding a solution to Ax= 0 when det A= 0; 10.2 Eigenvalues and Eigenvector; 10.3 Companion matrices and Vandermonde matrices; 10.4 Finding eigenvalues and Eigenvector by Danilevsky's method; 10.5 Error bounds for Danilevsky's method; 10.6 Rational matrices; 10.7 The demo programs eigen, c_eigen, and r_eigen; Software Exercises H; 11 Problems of Linear Programming; 11.1 Linear algebra using rational arithmetic 11.2 A more efficient method for solving rational linear equations |
| Record Nr. | UNINA-9910458146303321 |
Aberth Oliver
|
||
| Amsterdam ; ; Boston, : Academic Press, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to precise numerical methods [[electronic resource] /] / Oliver Aberth
| Introduction to precise numerical methods [[electronic resource] /] / Oliver Aberth |
| Autore | Aberth Oliver |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Academic Press, c2007 |
| Descrizione fisica | 1 online resource (267 p.) |
| Disciplina | 518.0285 |
| Soggetto topico |
Computer science - Mathematics
Numerical analysis - Data processing |
| ISBN |
1-280-96233-X
9786610962334 0-08-047120-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; 1 Introduction; 1.1 Open-source software; 1.2 Calling up a program; 1.3 Log files and print files; 1.4 More on log files; 1.5 The tilde notation for printed answers; 2 Computer Arithmetics; 2.1 Floating-point arithmetic; 2.2 Variable precision floating-point arithmetic; 2.3 Interval arithmetic; 2.4 Range arithmetic; 2.5 Practical range arithmetic; 2.6 Interval arithmetic notation; 2.7 Computing standard functions in range arithmetic; 2.8 Rational arithmetic; Software Exercises A; Notes and References; 3 Classification of Numerical Computation Problems; 3.1 A knotty problem
3.2 The impossibility of untying the knot 3.3 Repercussions from nonsolvable problem 3.1; 3.4 Some solvable and nonsolvable decimal place problems; 3.5 The solvable problems handled by calc; 3.6 Another nonsolvable problem; 3.7 The trouble with discontinuous functions; Notes and References; 4 Real-Valued Functions; 4.1 Elementary functions; Software Exercises B; 5 Computing Derivatives; 5.1 Power series of elementary functions; 5.2 An example of series evaluation; 5.3 Power series for elementary functions of several variables; 5.4 A more general method of generating power series 5.5 The demo program derivSoftware Exercises C; Notes and References; 6 Computing Integrals; 6.1 Computing a definite integral; 6.2 Formal interval arithmetic; 6.3 The demo program integ for computing ordinary definite integrals; 6.4 Taylor's remainder formula generalized; 6.5 The demo program mulint for higher dimensional integrals; 6.6 The demo program imprint for computing improper integrals; Software Exercises D; Notes and References; 7 Finding Where a Function f(x) is Zero; 7.1 Obtaining a solvable problem; 7.2 Using interval arithmetic for the problem; 7.3 Newton's method 7.4 Order of convergence Software Exercises E; 8 Finding Roots of Polynomials; 8.1 Polynomials; 8.2 A bound for the roots of a polynomial; 8.3 The Bairstow method for finding roots of a real polynomial; 8.4 Bounding the error of a rational polynomial's root approximations; 8.5 Finding accurate roots for a rational or a real polynomial; 8.6 The demo program roots; Software Exercises F; Notes and References; 9 Solving n Linear Equations in n Unknowns; 9.1 Notation; 9.2 Computation problems; 9.3 A method for solving linear equations; 9.4 Computing determinants 9.5 Finding the inverse of a square matrix 9.6 The demo programs equat, r_equat, and c_equat; Software Exercises G; Notes and References; 10 Eigenvalue and Eigenvector Problems; 10.1 Finding a solution to Ax= 0 when det A= 0; 10.2 Eigenvalues and Eigenvector; 10.3 Companion matrices and Vandermonde matrices; 10.4 Finding eigenvalues and Eigenvector by Danilevsky's method; 10.5 Error bounds for Danilevsky's method; 10.6 Rational matrices; 10.7 The demo programs eigen, c_eigen, and r_eigen; Software Exercises H; 11 Problems of Linear Programming; 11.1 Linear algebra using rational arithmetic 11.2 A more efficient method for solving rational linear equations |
| Record Nr. | UNINA-9910784659103321 |
|
Aberth Oliver
|
||
| Amsterdam ; ; Boston, : Academic Press, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to precise numerical methods / / Oliver Aberth
| Introduction to precise numerical methods / / Oliver Aberth |
| Autore | Aberth Oliver |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Boston, : Academic Press, c2007 |
| Descrizione fisica | 1 online resource (267 p.) |
| Disciplina | 518.0285 |
| Soggetto topico |
Computer science - Mathematics
Numerical analysis - Data processing |
| ISBN |
9786610962334
9781280962332 128096233X 9780080471204 008047120X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Acknowledgments; 1 Introduction; 1.1 Open-source software; 1.2 Calling up a program; 1.3 Log files and print files; 1.4 More on log files; 1.5 The tilde notation for printed answers; 2 Computer Arithmetics; 2.1 Floating-point arithmetic; 2.2 Variable precision floating-point arithmetic; 2.3 Interval arithmetic; 2.4 Range arithmetic; 2.5 Practical range arithmetic; 2.6 Interval arithmetic notation; 2.7 Computing standard functions in range arithmetic; 2.8 Rational arithmetic; Software Exercises A; Notes and References; 3 Classification of Numerical Computation Problems; 3.1 A knotty problem
3.2 The impossibility of untying the knot 3.3 Repercussions from nonsolvable problem 3.1; 3.4 Some solvable and nonsolvable decimal place problems; 3.5 The solvable problems handled by calc; 3.6 Another nonsolvable problem; 3.7 The trouble with discontinuous functions; Notes and References; 4 Real-Valued Functions; 4.1 Elementary functions; Software Exercises B; 5 Computing Derivatives; 5.1 Power series of elementary functions; 5.2 An example of series evaluation; 5.3 Power series for elementary functions of several variables; 5.4 A more general method of generating power series 5.5 The demo program derivSoftware Exercises C; Notes and References; 6 Computing Integrals; 6.1 Computing a definite integral; 6.2 Formal interval arithmetic; 6.3 The demo program integ for computing ordinary definite integrals; 6.4 Taylor's remainder formula generalized; 6.5 The demo program mulint for higher dimensional integrals; 6.6 The demo program imprint for computing improper integrals; Software Exercises D; Notes and References; 7 Finding Where a Function f(x) is Zero; 7.1 Obtaining a solvable problem; 7.2 Using interval arithmetic for the problem; 7.3 Newton's method 7.4 Order of convergence Software Exercises E; 8 Finding Roots of Polynomials; 8.1 Polynomials; 8.2 A bound for the roots of a polynomial; 8.3 The Bairstow method for finding roots of a real polynomial; 8.4 Bounding the error of a rational polynomial's root approximations; 8.5 Finding accurate roots for a rational or a real polynomial; 8.6 The demo program roots; Software Exercises F; Notes and References; 9 Solving n Linear Equations in n Unknowns; 9.1 Notation; 9.2 Computation problems; 9.3 A method for solving linear equations; 9.4 Computing determinants 9.5 Finding the inverse of a square matrix 9.6 The demo programs equat, r_equat, and c_equat; Software Exercises G; Notes and References; 10 Eigenvalue and Eigenvector Problems; 10.1 Finding a solution to Ax= 0 when det A= 0; 10.2 Eigenvalues and Eigenvector; 10.3 Companion matrices and Vandermonde matrices; 10.4 Finding eigenvalues and Eigenvector by Danilevsky's method; 10.5 Error bounds for Danilevsky's method; 10.6 Rational matrices; 10.7 The demo programs eigen, c_eigen, and r_eigen; Software Exercises H; 11 Problems of Linear Programming; 11.1 Linear algebra using rational arithmetic 11.2 A more efficient method for solving rational linear equations |
| Record Nr. | UNINA-9910960947003321 |
|
Aberth Oliver
|
||
| Amsterdam ; ; Boston, : Academic Press, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||