Author | Quarteroni, Alfio. author |
---|---|
Title | Scientific Computing with MATLAB [electronic resource] / by Alfio Quarteroni, Fausto Saleri |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-642-59339-0 |
Descript | IX, 257 p. 4 illus. online resource |
1. What canโt be ignored -- 1.1 Real numbers -- 1.2 Complex numbers -- 1.3 Matrices -- 1.4 Real functions -- 1.5 To err is not only human -- 1.6 A few more words about MATLAB -- 1.7 What we havenโt told you -- 1.8 Exercises -- 2. Nonlinear equations -- 2.1 The bisection method -- 2.2 The Newton method -- 2.3 Fixed point iterations -- 2.4 What we havenโt told you -- 2.5 Exercises -- 3. Approximation of functions and data -- 3.1 Interpolation -- 3.2 Piecewise linear interpolation -- 3.3 Approximation by spline functions -- 3.4 The least squares method -- 3.5 What we havenโt told you -- 3.6 Exercises -- 4. Numerical differentiation and integration -- 4.1 Approximation of function derivatives -- 4.2 Numerical integration -- 4.3 Simpson adaptive formula -- 4.4 What we havenโt told you -- 4.5 Exercises -- 5. Linear systems -- 5.1 The LU factorization method -- 5.2 The technique of pivoting -- 5.3 How accurate is the LU factorization? -- 5.4 How to solve a tridiagonal system -- 5.5 Iterative methods -- 5.5.1 How to construct an iterative method -- 5.6 When should an iterative method be stopped? -- 5.7 Richardson method -- 5.8 What we havenโt told you -- 5.9 Exercises -- 6. Eigenvalues and eigenvectors -- 6.1 The power method -- 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 havenโt told you -- 6.6 Exercises -- 7. Ordinary differential equations -- 7.1 The Cauchy problem -- 7.2 Euler methods -- 7.3 The Crank-Nicolson method -- 7.4 Zero-stability -- 7.5 Stability on unbounded intervals -- 7.6 High order methods -- 7.7 The predictor-corrector methods -- 7.8 Systems of differential equations -- 7.9 What we havenโt told you -- 7.10 Exercises -- 8. Numerical methods for boundary-value problems -- 8.1 Approximation of boundary-value problems -- 8.2 Finite differences in 2 dimensions -- 8.3 What we havenโt told you -- 8.4 Exercises -- 9. Solutions of the exercises -- 9.1 Chapter 1 -- 9.2 Chapter 2 -- 9.3 Chapter 3 -- 9.4 Chapter 4 -- 9.5 Chapter 5 -- 9.6 Chapter 6 -- 9.7 Chapter 7 -- 9.8 Chapter 8 -- Index of MATLAB Programs