Conjugate Direction Methods in Optimization

1. Front Matter

   Pages i-x

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2. Newton’s Method and the Gradient Method

   • Magnus Rudolph Hestenes

   Pages 1-80

3. Conjugate Direction Methods

   • Magnus Rudolph Hestenes

   Pages 81-149

4. Conjugate Gram-Schmidt Processes

   • Magnus Rudolph Hestenes

   Pages 150-230

5. Conjugate Gradient Algorithms

   • Magnus Rudolph Hestenes

   Pages 231-318

6. Back Matter

   Pages 319-325

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Shortly after the end of World War II high-speed digital computing machines were being developed. It was clear that the mathematical aspects of com­ putation needed to be reexamined in order to make efficient use of high-speed digital computers for mathematical computations. Accordingly, under the leadership of Min a Rees, John Curtiss, and others, an Institute for Numerical Analysis was set up at the University of California at Los Angeles under the sponsorship of the National Bureau of Standards. A similar institute was formed at the National Bureau of Standards in Washington, D. C. In 1949 J. Barkeley Rosser became Director of the group at UCLA for a period of two years. During this period we organized a seminar on the study of solu­ tions of simultaneous linear equations and on the determination of eigen­ values. G. Forsythe, W. Karush, C. Lanczos, T. Motzkin, L. J. Paige, and others attended this seminar. We discovered, for example, that even Gaus­ sian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed. During this period Lanczos developed his three-term relationship and I had the good fortune of suggesting the method of conjugate gradients. We dis­ covered afterward that the basic ideas underlying the two procedures are essentially the same. The concept of conjugacy was not new to me. In a joint paper with G. D.

• Mathematica
• Methode der konjugierten Richtungen
• algorithms
• numerical analysis
• optimization

• Department of Mathematics, University of California, Los Angeles, USA

  Magnus Rudolph Hestenes

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