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Softcover ISBN:  9780821815090 
Product Code:  SURV/9 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412371 
Product Code:  SURV/9.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821815090 
eBook ISBN:  9781470412371 
Product Code:  SURV/9.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: 9; 1963; 544 ppMSC: Primary 41
Many approximations are linear, that is, conform to the principle of superposition, and may profitably be studied by means of the theory of linear spaces. “Linear approximation” sets forth the pertinent parts of that theory, with particular attention to the key spaces \(C_n, B, K\), and Hilbert space, spaces which are powerful tools in the analysis, appraisal, and design of approximations, ranging from formulas of mechanical quadrature to approximations of operators by operators.
Because it affords a detailed treatment of a timely and important subject, “Linear approximation” is of interest to scientists and engineers as well as to mathematicians. The book includes worked illustrative examples and discussions of the rationale of its formulation of problems.

Table of Contents

Chapters

Introduction

1. Functionals in terms of derivatives

2. Applications

3. Linear continuous functionals on $C_n$

4. Functionals in terms of partial derivatives

5. Applications

6. Linear continuous functionals on $B$, $Z$, $K$

7. Functions of $m$ variables

8. Factors of operators

9. Efficient and strongly efficient approximation

10. Minimal response to error

11. The step functions $\theta $ and $\psi $

12. Stieltjes integrals, integration by parts, functions of bounded variation


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Many approximations are linear, that is, conform to the principle of superposition, and may profitably be studied by means of the theory of linear spaces. “Linear approximation” sets forth the pertinent parts of that theory, with particular attention to the key spaces \(C_n, B, K\), and Hilbert space, spaces which are powerful tools in the analysis, appraisal, and design of approximations, ranging from formulas of mechanical quadrature to approximations of operators by operators.
Because it affords a detailed treatment of a timely and important subject, “Linear approximation” is of interest to scientists and engineers as well as to mathematicians. The book includes worked illustrative examples and discussions of the rationale of its formulation of problems.

Chapters

Introduction

1. Functionals in terms of derivatives

2. Applications

3. Linear continuous functionals on $C_n$

4. Functionals in terms of partial derivatives

5. Applications

6. Linear continuous functionals on $B$, $Z$, $K$

7. Functions of $m$ variables

8. Factors of operators

9. Efficient and strongly efficient approximation

10. Minimal response to error

11. The step functions $\theta $ and $\psi $

12. Stieltjes integrals, integration by parts, functions of bounded variation