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1.

図書

図書
Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
出版情報: New York : Springer, c2000  xx, 654 p. ; 24 cm
シリーズ名: Texts in applied mathematics ; 37
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2.

図書

図書
Alfio Quarteroni, Alberto Valli
出版情報: Berlin ; London : Springer-Verlag, c1994  xvi, 543 p. ; 25 cm
シリーズ名: Springer series in computational mathematics ; 23
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3.

図書

図書
Alfio Quarteroni, Fausto Saleri, Paola Gervasio
出版情報: Berlin : Springer, c2010  xvi, 360 p. ; 24 cm
シリーズ名: Texts in computational science and engineering ; 2
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目次情報: 続きを見る
What can't be ignored / 1:
The MATLAB and Octave environments / 1.1:
Real numbers / 1.2:
How we represent them / 1.2.1:
How we operate with floating-point numbers / 1.2.2:
Complex numbers / 1.3:
Matrices / 1.4:
Vectors / 1.4.1:
Real functions / 1.5:
The zeros / 1.5.1:
Polynomials / 1.5.2:
Integration and differentiation / 1.5.3:
To err is not only human / 1.6:
Talking about costs / 1.6.1:
The MATLAB language / 1.7:
MATLAB statements / 1.7.1:
Programming in MATLAB / 1.7.2:
Examples of differences between MATLAB and Octave languages / 1.7.3:
What we haven't told you / 1.8:
Exercises / 1.9:
Nonlinear equations / 2:
Some representative problems / 2.1:
The bisection method / 2.2:
The Newton method / 2.3:
How to terminate Newton's iterations / 2.3.1:
The Newton method for systems of nonlinear equations / 2.3.2:
Fixed point iterations / 2.4:
How to terminate fixed point iterations / 2.4.1:
Acceleration using Aitken's method / 2.5:
Algebraic polynomials / 2.6:
Hörner's algorithm / 2.6.1:
The Newton-Hörner method / 2.6.2:
Approximation of functions and data / 2.7:
Approximation by Taylor's polynomials / 3.1:
Interpolation / 3.3:
Lagrangian polynomial interpolation / 3.3.1:
Stability of polynomial interpolation / 3.3.2:
Interpolation at Chebyshev nodes / 3.3.3:
Trigonometric interpolation and FFT / 3.3.4:
Piecewise linear interpolation / 3.4:
Approximation by spline functions / 3.5:
The least-squares method / 3.6:
Numerical differentiation and integration / 3.7:
Approximation of function derivatives / 4.1:
Numerical integration / 4.3:
Midpoint formula / 4.3.1:
Trapezoidal formula / 4.3.2:
Simpson formula / 4.3.3:
Interpolatory quadratures / 4.4:
Simpson adaptive formula / 4.5:
Linear systems / 4.6:
Linear system and complexity / 5.1:
The LU factorization method / 5.3:
The pivoting technique / 5.4:
How accurate is the solution of a linear system? / 5.5:
How to solve a tridiagonal system / 5.6:
Overdetermined systems / 5.7:
What is hidden behind the MATLAB command / 5.8:
Iterative methods / 5.9:
How to construct an iterative method / 5.9.1:
Richardson and gradient methods / 5.10:
The conjugate gradient method / 5.11:
When should an iterative method be stopped? / 5.12:
To wrap-up: direct or iterative? / 5.13:
Eigenvalues and eigenvectors / 5.14:
The power method / 6.1:
Convergence analysis / 6.2.1:
Generalization of the power method / 6.3:
How to compute the shift / 6.4:
Computation of all the eigenvalues / 6.5:
Ordinary differential equations / 6.6:
The Cauchy problem / 7.1:
Euler methods / 7.3:
The Crank-Nicolson method / 7.3.1:
Zero-stability / 7.5:
Stability on unbounded intervals / 7.6:
The region of absolute stability / 7.6.1:
Absolute stability controls perturbations / 7.6.2:
High order methods / 7.7:
The predictor-corrector methods / 7.8:
Systems of differential equations / 7.9:
Some examples / 7.10:
The spherical pendulum / 7.10.1:
The three-body problem / 7.10.2:
Some stiff problems / 7.10.3:
Numerical approximation of boundary-value problems / 7.11:
Approximation of boundary-value problems / 8.1:
Finite difference approximation of the one-dimensional Poisson problem / 8.2.1:
Finite difference approximation of a convection-dominated problem / 8.2.2:
Finite element approximation of the one-dimensional Poisson problem / 8.2.3:
Finite difference approximation of the two-dimensional Poisson problem / 8.2.4:
Consistency and convergence of finite difference discretization of the Poisson problem / 8.2.5:
Finite difference approximation of the one-dimensional heat equation / 8.2.6:
Finite element approximation of the one-dimensional heat equation / 8.2.7:
Hyperbolic equations: a scalar pure advection problem / 8.3:
Finite difference discretization of the scalar transport equation / 8.3.1:
Finite difference analysis for the scalar transport equation / 8.3.2:
Finite element space discretization of the scalar advection equation / 8.3.3:
The wave equation / 8.4:
Finite difference approximation of the wave equation / 8.4.1:
Solutions of the exercises / 8.5:
References / 9.1:
Index
What can't be ignored / 1:
The MATLAB and Octave environments / 1.1:
Real numbers / 1.2:
4.

図書

図書
A. クアルテローニ, F. サレリ, P. ジェルヴァシオ著 ; 加古孝, 千葉文浩訳
出版情報: 東京 : 丸善出版, 2014.12  xvi, 502p ; 22cm
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目次情報: 続きを見る
第1章 : 必要な予備知識
第2章 : 非線形方程式系
第3章 : 関数とデータの近似
第4章 : 数値微分と数値積分
第5章 : 線形方程式系
第6章 : 固有値と固有ベクトル
第7章 : 数値的最適化
第8章 : 常微分方程式
第9章 : 境界値問題の数値近似解法
第10章 : 練習問題の解答
第1章 : 必要な予備知識
第2章 : 非線形方程式系
第3章 : 関数とデータの近似
概要: コンピュータを用いた科学技術計算がどのように行われるかMATLABとOctaveを用いて具体的に解説。各章の初めに対象とする様々な現象とそれを取り扱うための数理モデルが具体的に紹介されている。理工系大学の初学年で学ぶ微積分と線形代数に基づい て数値的方法の基礎をマスターできる科学技術計算の実践的入門書。 続きを見る
5.

電子ブック

EB
Bernardo Cockburn, Bernardo Cockburn, Centro internazionale matematico estivo., B. Cockburn, C. Johnson, Alfio Quarteroni, C. -W. Shu, E. Tadmor
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 1998
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6.

電子ブック

EB
Alfio Quarteroni, Bertrand Maury
出版情報: SpringerLink Books - AutoHoldings , Springer Milan, 2013
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7.

電子ブック

EB
Alfio Quarteroni, Paola Gervasio, Fausto Saleri
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2010
所蔵情報: loading…
目次情報: 続きを見る
What can't be ignored / 1:
The MATLAB and Octave environments / 1.1:
Real numbers / 1.2:
How we represent them / 1.2.1:
How we operate with floating-point numbers / 1.2.2:
Complex numbers / 1.3:
Matrices / 1.4:
Vectors / 1.4.1:
Real functions / 1.5:
The zeros / 1.5.1:
Polynomials / 1.5.2:
Integration and differentiation / 1.5.3:
To err is not only human / 1.6:
Talking about costs / 1.6.1:
The MATLAB language / 1.7:
MATLAB statements / 1.7.1:
Programming in MATLAB / 1.7.2:
Examples of differences between MATLAB and Octave languages / 1.7.3:
What we haven't told you / 1.8:
Exercises / 1.9:
Nonlinear equations / 2:
Some representative problems / 2.1:
The bisection method / 2.2:
The Newton method / 2.3:
How to terminate Newton's iterations / 2.3.1:
The Newton method for systems of nonlinear equations / 2.3.2:
Fixed point iterations / 2.4:
How to terminate fixed point iterations / 2.4.1:
Acceleration using Aitken's method / 2.5:
Algebraic polynomials / 2.6:
Hörner's algorithm / 2.6.1:
The Newton-Hörner method / 2.6.2:
Approximation of functions and data / 2.7:
Approximation by Taylor's polynomials / 3.1:
Interpolation / 3.3:
Lagrangian polynomial interpolation / 3.3.1:
Stability of polynomial interpolation / 3.3.2:
Interpolation at Chebyshev nodes / 3.3.3:
Trigonometric interpolation and FFT / 3.3.4:
Piecewise linear interpolation / 3.4:
Approximation by spline functions / 3.5:
The least-squares method / 3.6:
Numerical differentiation and integration / 3.7:
Approximation of function derivatives / 4.1:
Numerical integration / 4.3:
Midpoint formula / 4.3.1:
Trapezoidal formula / 4.3.2:
Simpson formula / 4.3.3:
Interpolatory quadratures / 4.4:
Simpson adaptive formula / 4.5:
Linear systems / 4.6:
Linear system and complexity / 5.1:
The LU factorization method / 5.3:
The pivoting technique / 5.4:
How accurate is the solution of a linear system? / 5.5:
How to solve a tridiagonal system / 5.6:
Overdetermined systems / 5.7:
What is hidden behind the MATLAB command / 5.8:
Iterative methods / 5.9:
How to construct an iterative method / 5.9.1:
Richardson and gradient methods / 5.10:
The conjugate gradient method / 5.11:
When should an iterative method be stopped? / 5.12:
To wrap-up: direct or iterative? / 5.13:
Eigenvalues and eigenvectors / 5.14:
The power method / 6.1:
Convergence analysis / 6.2.1:
Generalization of the power method / 6.3:
How to compute the shift / 6.4:
Computation of all the eigenvalues / 6.5:
Ordinary differential equations / 6.6:
The Cauchy problem / 7.1:
Euler methods / 7.3:
The Crank-Nicolson method / 7.3.1:
Zero-stability / 7.5:
Stability on unbounded intervals / 7.6:
The region of absolute stability / 7.6.1:
Absolute stability controls perturbations / 7.6.2:
High order methods / 7.7:
The predictor-corrector methods / 7.8:
Systems of differential equations / 7.9:
Some examples / 7.10:
The spherical pendulum / 7.10.1:
The three-body problem / 7.10.2:
Some stiff problems / 7.10.3:
Numerical approximation of boundary-value problems / 7.11:
Approximation of boundary-value problems / 8.1:
Finite difference approximation of the one-dimensional Poisson problem / 8.2.1:
Finite difference approximation of a convection-dominated problem / 8.2.2:
Finite element approximation of the one-dimensional Poisson problem / 8.2.3:
Finite difference approximation of the two-dimensional Poisson problem / 8.2.4:
Consistency and convergence of finite difference discretization of the Poisson problem / 8.2.5:
Finite difference approximation of the one-dimensional heat equation / 8.2.6:
Finite element approximation of the one-dimensional heat equation / 8.2.7:
Hyperbolic equations: a scalar pure advection problem / 8.3:
Finite difference discretization of the scalar transport equation / 8.3.1:
Finite difference analysis for the scalar transport equation / 8.3.2:
Finite element space discretization of the scalar advection equation / 8.3.3:
The wave equation / 8.4:
Finite difference approximation of the wave equation / 8.4.1:
Solutions of the exercises / 8.5:
References / 9.1:
Index
What can't be ignored / 1:
The MATLAB and Octave environments / 1.1:
Real numbers / 1.2:
8.

電子ブック

EB
Alfio Quarteroni, Fausto Saleri
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2014
所蔵情報: loading…
9.

電子ブック

EB
Alfio Quarteroni, Tom Hou, Claude Le Bris
出版情報: SpringerLink Books - AutoHoldings , Springer Milan, 2009
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目次情報: 続きを見る
Introduction
A brief survey on partial differential equations / 1:
Elliptic equations / 2:
The Galerkin finite element method for elliptic problems / 3:
Spectral methods / 4:
Diffusion-transport-reaction equations / 5:
Parabolic equations / 6:
Finite differences for hyperbolic equations / 7:
Finite elements and spectral methods for hyperbolic equations / 8:
Nonlinear hyperbolic problems / 9:
The Navier-Stokes equations / 10:
Finite element programming / 11:
Generation of 1D and 2D grids / 12:
The finite volume method / 13:
Domain decomposition method / 14:
Optimal control problems for partial differential equations / 15:
Reduced basis methods / 16:
Elements of functional analysis / 17:
Solution of algebraic systems / 18:
Introduction
A brief survey on partial differential equations / 1:
Elliptic equations / 2:
10.

電子ブック

EB
Alfio Quarteroni
出版情報: SpringerLink Books - AutoHoldings , Springer Milan, 2014
所蔵情報: loading…
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