Basic Numerical Mathematics

1. Front Matter

   Pages 1-11

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2. Manipulation of Vectors and Matrices

   • John Todd

   Pages 13-15

3. Norms of Vectors and Matrices

   • John Todd

   Pages 16-18

4. Induced Norms

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   Pages 19-28

5. The Inversion Problem I: Theoretical Arithmetic

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   Pages 29-43

6. The Inversion Problem II: Practical Computation

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   Pages 44-52

7. The Characteristic Value Problem—Generalities

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   Pages 53-64

8. The Power Method, Deflation, Inverse Iteration

   • John Todd

   Pages 65-70

9. Characteristic Values

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   Pages 71-82

10. Iterative Methods for the Solution of Systems Ax = b

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    Pages 83-98

11. Application: Solution of a Boundary Value Problem

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    Pages 99-104

12. Application: Least Squares Curve Fitting

    • John Todd

    Pages 105-109

13. Singular Value Decomposition and Pseudo-Inverses

    • John Todd

    Pages 110-115

14. Back Matter

    Pages 117-216

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There is no doubt nowadays that numerical mathematics is an essential component of any educational program. It is probably more efficient to present such material after a reasonable competence in (at least) linear algebra and calculus has already been attained - but at this stage those not specializ­ ing in numerical mathematics are often interested in getting more deeply into their chosen field than in developing skills for later use. An alternative approach is to incorporate the numerical aspects of linear algebra and cal­ culus as these subjects are being developed. Long experience has persuaded us that a third attack on this problem is the best and this is developed in the present two volumes, which are, however, easily adaptable to other circum­ stances. The approach we prefer is to treat the numerical aspects separately, but after some theoretical background. This is often desirable because of the shortage of persons qualified to present the combined approach and also because the numerical approach provides an often welcome change which, however, in addition, can lead to better appreciation of the fundamental con­ cepts. For instance, in a 6-quarter course in Calculus and Linear Algebra, the material in Volume 1 can be handled in the third quarter and that in Volume 2 in the fifth or sixth quarter.

• calculus
• curve fitting
• education
• fitting
• linear algebra
• mathematics
• numerical analysis

• California Institute of Technology, USA

  John Todd

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