Approximation techniques for engineers /
This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial funct...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press,
[2017]
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| Edition: | Second edition. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice. |
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| Item Description: | Previous edition: 2007. <P><strong>I Data approximations</strong></p> <p>1 Classical interpolation methods</p> <p>1.1 Newton interpolation</p> <p>1.2 Lagrange interpolation</p> <p>1.3 Hermite interpolation</p> <p>1.3.1 Computational example</p> <p>1.4 Interpolation of functions of two variables with polynomials</p> <p>References</p> <p> <p>2 Approximation with splines </p> <p>2.1 Natural cubic splines</p> <p>2.2 Bezier splines</p> <p>2.3 Approximation with B-splines</p> <p>2.4 Surface spline approximation</p> <p>References</p> <p> <p>3 Least squares approximation</p> <p>3.1 The least squares principle</p> <p>3.2 Linear least squares approximation</p> <p>3.3 Polynomial least squares approximation</p> <p>3.4 Computational example</p> <p>3.5 Exponential and logarithmic least squares approximations</p> <p>3.6 Nonlinear least squares approximation</p> <p>3.7 Trigonometric least squares approximation</p> <p>3.8 Directional least squares approximation</p> <p>3.9 Weighted least squares approximation</p> <p>References</p> <p> <p>4 Approximation of functions</p> <p>4.1 Least squares approximation of functions</p> <p>4.2 Approximation with Legendre polynomials</p> <p>4.3 Chebyshev approximation</p> <p>4.4 Fourier approximation</p> <p>4.5 Pad'e approximation</p> <p>4.6 Approximating matrix functions</p> <p>References</p> <p> <p>5 Numerical differentiation</p> <p>5.1 Finite difference formulae</p> <p>5.2 Higher order derivatives</p> <p>5.3 Richardson's extrapolation</p> <p>5.4 Multipoint finite difference formulae</p> <p>References</p> <p> <p>6 Numerical integration</p> <p>6.1 The Newton-Cotes class</p> <p>6.2 Advanced Newton-Cotes methods</p> <p>6.3 Gaussian quadrature</p> <p>6.4 Integration of functions of multiple variables</p> <p>6.5 Chebyshev quadrature</p> <p>6.6 Numerical integration of periodic functions</p> <p>References</p> <p><strong>II Approximate solutions</strong></p> <p>7 Nonlinear equations in one variable</p> <p>7.1 General equations</p> <p>7.2 Newton's method</p> <p>7.3 Solution of algebraic equations</p> <p>7.4 Aitken's acceleration</p> <p>References</p> <p> <p>8 Systems of nonlinear equations</p> <p>8.1 The generalized fixed point method</p> <p>8.2 The method of steepest descent</p> <p>8.3 The generalization of Newton's method</p> <p>8.4 Quasi-Newton method</p> <p>8.5 Nonlinear static analysis application</p> <p>References</p> <p> <p>9 Iterative solution of linear systems</p> <p>9.1 Iterative solution of linear systems</p> <p>9.2 Splitting methods</p> <p>9.3 Ritz-Galerkin method</p> <p>9.4 Conjugate gradient method</p> <p>9.5 Preconditioning techniques</p> <p>9.6 Biconjugate gradient method</p> <p>9.7 Least squares systems</p> <p>9.8 The minimum residual approach</p> <p>9.9 Algebraic multigrid method</p> <p>9.10 Linear static analysis application</p> <p>References</p> <p> <p>10 Approximate solution of eigenvalue problems</p> <p>10.1 Classical iterations</p> <p>10.2 The Rayleigh-Ritz procedure</p> <p>10.3 The Lanczos method</p> <p>10.4 The solution of the tridiagonal eigenvalue problem</p> <p>10.5 The biorthogonal Lanczos method</p> <p>10.6 The Arnoldi method</p> <p>10.7 The block Lanczos method</p> <p>10.7.1 Preconditioned block Lanczos method</p> <p>10.8 Normal modes analysis application</p> <p>References</p> <p> <p>11 Initial value problems</p> <p>11.1 Solution of initial value problems</p> <p>11.2 Single-step methods</p> <p>11.3 Multistep methods</p> <p>11.4 Initial value problems of systems of ordinary differential equations</p> <p>11.5 Initial value problems of higher order ordinary differential equations</p> <p>11.6 Linearization of second order initial value problems</p> <p>11.7 Transient response analysis application</p> <p>References</p> <p> <p>12 Boundary value problems</p> <p>12.1 Boundary value problems of ordinary differential equations</p> <p>12.2 The finite difference method for boundary value problems of</p> <p>ordinary differential equations</p> <p>12.3 Boundary value problems of partial differential equations</p> <p>12.4 The finite difference method for boundary value problems of</p> <p>partial differential equations</p> <p>12.5 The finite element method</p> <p>12.6 Finite element analysis of three-dimensional continuum</p> <p>12.7 Fluid-structure interaction application</p> <p>References </p> <p> <p>13 Integral equations</p> <p>13.1 Converting initial value problems to integral equations</p> <p>13.2 Converting boundary value problems to integral equations</p> <p>13.3 Classification of integral equations</p> <p>13.4 Fredholm solution</p> <p>13.5 Neumann approximation</p> <p>13.6 Nystrom method</p> <p>13.7 Nonlinear integral equations </p> <p>13.8 Integro-differential equations</p> <p>13.8.1 Computational example</p> <p>13.9 Boundary integral method application</p> <p>References</p> <p> <p>14 Mathematical optimization</p> <p>14.1 Existence of solution</p> <p>14.2 Penalty method</p> <p>14.3 Quadratic optimization</p> <p>14.4 Gradient based methods</p> <p>14.5 Global optimization</p> <p>14.6 Topology optimization</p> <p>14.7 Structural compliance application</p> <p>References</p> <p> <p>List of figures</p> <p>List of tables</p> <p>Annotation</p> <p>Index</p> <p>Closing remarks</p> |
| Physical Description: | 1 online resource (xix, 366 pages) : illustrations (black and white) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781351792721 1351792725 9781138700055 1138700053 9781351792714 1351792717 9781351792707 1351792709 9781315205007 1315205009 |