TY  - BOOK
AU  - Quarteroni,Alfio
TI  - Scientific computing with MATLAB and Octave
SN  - 9788184894301 (pb)
U1  - 004.076 
PY  - 2006///
CY  - Berlin, New York
PB  - Springer
KW  - Science
KW  - Data processing
N1  - What can't be ignored
1.1 Real numbers
1.1.1 How we represent them
1.1.2 How we operate with floating-point numbers
1.2 Complex numbers
1.3 Matrices
1.3.1 Vectors
1.4 Real functions
1.4.1 The zeros
1.4.2 Polynomials
1.4.3 Integration and differentiatior
1.5 To err is not only human
1.5.1 Talking about costs
1.6 The MATLAB and Octave environments
1.7 The MATLAB language
1.7.1 MATLAB statements
1.7.2 Programming in MATLAB
1.7.3 Examples of differences between MATLAB
and Octave languages .
1.8 What we haven't told you
1.9 Exercises
Nonlinear equations
2.1 The bisection method
2.2 The Newton method .
2.2.1 How to terminate Newton's iterations
2.2.2 The Newton method for systems of nonlinear
equations
2.3 Fixed point iterations
2.3.1 How to terminate fixed point iterations
2.4 Acceleration using Aitken niethod
2.5 Algebraic polynoinials
2.5.1 Homer's algorithm
2.5.2 The Newton-Horner method
2.6 What we haven't told you
2.7 Exercises
Approximation of functions and data
3.1 Interpolation
3.1.1 Lagrangian polynomial interpolation
3.1.2 Chebyshev interpolation.
3.1.3 Trigonometric interpolation and FFT
3.2 Piecewise linear interpolation
3.3 Approximation by spline functions
3.4 The least-squares method.
3.5 What we haven't told you
3.6 Exercises
Numerical differentiation and integration
4.1 Approximation of function derivatives
4.2 Numerical integration
4.2.1 Midpoint formula
4.2.2 Trapezoidal formula
4.2.3 Simpson formula
4.3 Interpolatory quadratures
4.4 Simpson adaptive formula
4.5 What we haven't told you
4.6 Exercises
Linear systems
5.1 The LU factorization method
5.2 The pivoting technique
5.3 How accurate is the LU factorization?
5.4 How to solve a tridiagonal system
5.5 Overdetermined systems.
5.6 What is hidden behind the command ^
5.7 Iterative methods
5.7.1 How to construct an iterative method .
5.8 Richardson and gradient methods
5.9 The conjugate gradient method . .
5.10 When should an iterative method be stopped?
5.11 To wrap-up: direct or iterative?
5.12 What we haven't told you
5.13 Exercises
Eigenvalues and eigenvectors
6.1 The power method
6.1.1 Convergence analysis
6.2 Generalization of the power method
6.3 How to compute the shift
6.4 Computation of all the eigenvalues.
6.5 What we haven't told you
6.6 Exercises
Ordinary differential equations
7.1 The Cauchy problem
7.2 Euler methods
7.2.1 Convergence analysis
7.3 The Crank-Nicolson method
7.4 Zero-stability
7.5 Stability on unbounded intervals
7.5.1 The region of absolute stability
7.5.2 Absolute stability controls perturbations
7.6 High order methods
7.7 The predictor-corrector methods
7.8 Systems of differential equations
7.9 Some examples
7.9.1 The spherical pendulum
7.9.2 The three-body problem
7.9.3 Some stiff problems
7.10 What we haven't told you
7.11 Exercises
Numerical methods for (initial-)boundary-value
problems
8.1 Approximation of boundary-value problems
8.1.1 Approximation by finite differences
8.1.2 Approximation by finite elements
8.1.3 Approximation by finite differences
of two-dimensional problems
8.1.4 Consistency and convergence
8.2 Finite difference approximation of the heat equation
8.3 The wave equation
8.3.1 Approximation by finite differences
8.4 What we haven't told you
8.5 ExercisesWhat can't be ignored
1.1 Real numbers
1.1.1 How we represent them
1.1.2 How we operate with floating-point numbers
1.2 Complex numbers
1.3 Matrices
1.3.1 Vectors
1.4 Real functions
1.4.1 The zeros
1.4.2 Polynomials
1.4.3 Integration and differentiatior
1.5 To err is not only human
1.5.1 Talking about costs
1.6 The MATLAB and Octave environments
1.7 The MATLAB language
1.7.1 MATLAB statements
1.7.2 Programming in MATLAB
1.7.3 Examples of differences between MATLAB
and Octave languages .
1.8 What we haven't told you
1.9 Exercises
Nonlinear equations
2.1 The bisection method
2.2 The Newton method .
2.2.1 How to terminate Newton's iterations
2.2.2 The Newton method for systems of nonlinear
equations
2.3 Fixed point iterations
2.3.1 How to terminate fixed point iterations
2.4 Acceleration using Aitken niethod
2.5 Algebraic polynoinials
2.5.1 Homer's algorithm
2.5.2 The Newton-Horner method
2.6 What we haven't told you
2.7 Exercises
Approximation of functions and data
3.1 Interpolation
3.1.1 Lagrangian polynomial interpolation
3.1.2 Chebyshev interpolation.
3.1.3 Trigonometric interpolation and FFT
3.2 Piecewise linear interpolation
3.3 Approximation by spline functions
3.4 The least-squares method.
3.5 What we haven't told you
3.6 Exercises
Numerical differentiation and integration
4.1 Approximation of function derivatives
4.2 Numerical integration
4.2.1 Midpoint formula
4.2.2 Trapezoidal formula
4.2.3 Simpson formula
4.3 Interpolatory quadratures
4.4 Simpson adaptive formula
4.5 What we haven't told you
4.6 Exercises
Linear systems
5.1 The LU factorization method
5.2 The pivoting technique
5.3 How accurate is the LU factorization?
5.4 How to solve a tridiagonal system
5.5 Overdetermined systems.
5.6 What is hidden behind the command ^
5.7 Iterative methods
5.7.1 How to construct an iterative method .
5.8 Richardson and gradient methods
5.9 The conjugate gradient method . .
5.10 When should an iterative method be stopped?
5.11 To wrap-up: direct or iterative?
5.12 What we haven't told you
5.13 Exercises
Eigenvalues and eigenvectors
6.1 The power method
6.1.1 Convergence analysis
6.2 Generalization of the power method
6.3 How to compute the shift
6.4 Computation of all the eigenvalues.
6.5 What we haven't told you
6.6 Exercises
Ordinary differential equations
7.1 The Cauchy problem
7.2 Euler methods
7.2.1 Convergence analysis
7.3 The Crank-Nicolson method
7.4 Zero-stability
7.5 Stability on unbounded intervals
7.5.1 The region of absolute stability
7.5.2 Absolute stability controls perturbations
7.6 High order methods
7.7 The predictor-corrector methods
7.8 Systems of differential equations
7.9 Some examples
7.9.1 The spherical pendulum
7.9.2 The three-body problem
7.9.3 Some stiff problems
7.10 What we haven't told you
7.11 Exercises
Numerical methods for (initial-)boundary-value
problems
8.1 Approximation of boundary-value problems
8.1.1 Approximation by finite differences
8.1.2 Approximation by finite elements
8.1.3 Approximation by finite differences
of two-dimensional problems
8.1.4 Consistency and convergence
8.2 Finite difference approximation of the heat equation
8.3 The wave equation
8.3.1 Approximation by finite differences
8.4 What we haven't told you
8.5 ExercisesWhat can't be ignored
1.1 Real numbers
1.1.1 How we represent them
1.1.2 How we operate with floating-point numbers
1.2 Complex numbers
1.3 Matrices
1.3.1 Vectors
1.4 Real functions
1.4.1 The zeros
1.4.2 Polynomials
1.4.3 Integration and differentiatior
1.5 To err is not only human
1.5.1 Talking about costs
1.6 The MATLAB and Octave environments
1.7 The MATLAB language
1.7.1 MATLAB statements
1.7.2 Programming in MATLAB
1.7.3 Examples of differences between MATLAB
and Octave languages .
1.8 What we haven't told you
1.9 Exercises
Nonlinear equations
2.1 The bisection method
2.2 The Newton method .
2.2.1 How to terminate Newton's iterations
2.2.2 The Newton method for systems of nonlinear
equations
2.3 Fixed point iterations
2.3.1 How to terminate fixed point iterations
2.4 Acceleration using Aitken niethod
2.5 Algebraic polynoinials
2.5.1 Homer's algorithm
2.5.2 The Newton-Horner method
2.6 What we haven't told you
2.7 Exercises
Approximation of functions and data
3.1 Interpolation
3.1.1 Lagrangian polynomial interpolation
3.1.2 Chebyshev interpolation.
3.1.3 Trigonometric interpolation and FFT
3.2 Piecewise linear interpolation
3.3 Approximation by spline functions
3.4 The least-squares method.
3.5 What we haven't told you
3.6 Exercises
Numerical differentiation and integration
4.1 Approximation of function derivatives
4.2 Numerical integration
4.2.1 Midpoint formula
4.2.2 Trapezoidal formula
4.2.3 Simpson formula
4.3 Interpolatory quadratures
4.4 Simpson adaptive formula
4.5 What we haven't told you
4.6 Exercises
Linear systems
5.1 The LU factorization method
5.2 The pivoting technique
5.3 How accurate is the LU factorization?
5.4 How to solve a tridiagonal system
5.5 Overdetermined systems.
5.6 What is hidden behind the command ^
5.7 Iterative methods
5.7.1 How to construct an iterative method .
5.8 Richardson and gradient methods
5.9 The conjugate gradient method . .
5.10 When should an iterative method be stopped?
5.11 To wrap-up: direct or iterative?
5.12 What we haven't told you
5.13 Exercises
Eigenvalues and eigenvectors
6.1 The power method
6.1.1 Convergence analysis
6.2 Generalization of the power method
6.3 How to compute the shift
6.4 Computation of all the eigenvalues.
6.5 What we haven't told you
6.6 Exercises
Ordinary differential equations
7.1 The Cauchy problem
7.2 Euler methods
7.2.1 Convergence analysis
7.3 The Crank-Nicolson method
7.4 Zero-stability
7.5 Stability on unbounded intervals
7.5.1 The region of absolute stability
7.5.2 Absolute stability controls perturbations
7.6 High order methods
7.7 The predictor-corrector methods
7.8 Systems of differential equations
7.9 Some examples
7.9.1 The spherical pendulum
7.9.2 The three-body problem
7.9.3 Some stiff problems
7.10 What we haven't told you
7.11 Exercises
Numerical methods for (initial-)boundary-value
problems
8.1 Approximation of boundary-value problems
8.1.1 Approximation by finite differences
8.1.2 Approximation by finite elements
8.1.3 Approximation by finite differences
of two-dimensional problems
8.1.4 Consistency and convergence
8.2 Finite difference approximation of the heat equation
8.3 The wave equation
8.3.1 Approximation by finite differences
8.4 What we haven't told you
8.5 Exercises
ER  -