Hardcover ISBN:  9780821842034 
Product Code:  SURV/141 
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eBook ISBN:  9781470413682 
Product Code:  SURV/141.E 
List Price:  $125.00 
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AMS Member Price:  $100.00 
Hardcover ISBN:  9780821842034 
eBook: ISBN:  9781470413682 
Product Code:  SURV/141.B 
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Hardcover ISBN:  9780821842034 
Product Code:  SURV/141 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413682 
Product Code:  SURV/141.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821842034 
eBook ISBN:  9781470413682 
Product Code:  SURV/141.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 141; 2007; 349 ppMSC: Primary 41
In this book, a new approach to approximation procedures is developed. This new approach is characterized by the common feature that the procedures are accurate without being convergent as the mesh size tends to zero. This lack of convergence is compensated for by the flexibility in the choice of approximating functions, the simplicity of multidimensional generalizations, and the possibility of obtaining explicit formulas for the values of various integral and pseudodifferential operators applied to approximating functions.
The developed techniques allow the authors to design new classes of highorder quadrature formulas for integral and pseudodifferential operators, to introduce the concept of approximate wavelets, and to develop new efficient numerical and seminumerical methods for solving boundary value problems of mathematical physics.
The book is intended for researchers interested in approximation theory and numerical methods for partial differential and integral equations.
ReadershipGraduate students and research mathematicians interested in approximation theory and numerical methods.

Table of Contents

Chapters

1. Quasiinterpolation

2. Error estimates for quasiinterpolation

3. Various basis functions — examples and constructions

4. Approximation of integral operators

5. Cubature of diffraction, elastic, and hydrodynamic potentials

6. Some other cubature problems

7. Approximation by Gaussians

8. Approximate wavelets

9. Cubature over bounded domains

10. More general grids

11. Scattered data approximate approximations

12. Numerical algorithms based upon approximate approximations — linear problems

13. Numerical algorithms based upon approximate approximations — nonlinear problems


Additional Material

Reviews

Altogether, this is an interesting book, most useful for the approximation theorist as well as for the practitioner who appreciates that approximate approximations are a useful and practicable alternative to the classical ideas of approximations with small stepsizes and ultimately convergence theorems.
Mathematical Reviews


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In this book, a new approach to approximation procedures is developed. This new approach is characterized by the common feature that the procedures are accurate without being convergent as the mesh size tends to zero. This lack of convergence is compensated for by the flexibility in the choice of approximating functions, the simplicity of multidimensional generalizations, and the possibility of obtaining explicit formulas for the values of various integral and pseudodifferential operators applied to approximating functions.
The developed techniques allow the authors to design new classes of highorder quadrature formulas for integral and pseudodifferential operators, to introduce the concept of approximate wavelets, and to develop new efficient numerical and seminumerical methods for solving boundary value problems of mathematical physics.
The book is intended for researchers interested in approximation theory and numerical methods for partial differential and integral equations.
Graduate students and research mathematicians interested in approximation theory and numerical methods.

Chapters

1. Quasiinterpolation

2. Error estimates for quasiinterpolation

3. Various basis functions — examples and constructions

4. Approximation of integral operators

5. Cubature of diffraction, elastic, and hydrodynamic potentials

6. Some other cubature problems

7. Approximation by Gaussians

8. Approximate wavelets

9. Cubature over bounded domains

10. More general grids

11. Scattered data approximate approximations

12. Numerical algorithms based upon approximate approximations — linear problems

13. Numerical algorithms based upon approximate approximations — nonlinear problems

Altogether, this is an interesting book, most useful for the approximation theorist as well as for the practitioner who appreciates that approximate approximations are a useful and practicable alternative to the classical ideas of approximations with small stepsizes and ultimately convergence theorems.
Mathematical Reviews