High powers of matrices

ABSTRACT

At the conference APL87 held in Dallas, Dr. Tama Traberman referred to problems associated with Markov Processes. Her example showed a Markov matrix and gave an algorithm for finding powers of that matrix. In this paper we discuss two different ways of decreasing the amount of arithmetic necessary to arrive at the results.

REFERENCES

• 1: Curtis, Charles W.: Linear Algebra: an introductory approach. Allyn and Bacon, Inc., 1974.
• 2: V. A. Dyck , Smith , Barbara Lawson, Introduction to Computing, Prentice Hall Professional Technical Reference, 1979
• 3: Dyck, V.A., Lawson, J-D., Smith, J-A., and Beach, R.J.: Computing: an introduction to structured problem solving using Pascal. Reston Publishing Company, Inc., 1982.
• 4: Kenneth E. Iverson, A dictionary of APL, ACM SIGAPL APL Quote Quad, v.18 n.1, p.5-40, September 1, 1987 [doi>10.1145/36983.36984]
• 5: Schneider, H. and Barker, G-P.: Matrices and Linear Algebra. Holt, Rinehart and Winston, Inc., 1968.
• 6: Tama Traberman, A model for teaching APL: moving into the fast lane, ACM SIGAPL APL Quote Quad, v.17 n.4, p.88-93, May 1987

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

General Terms:
Algorithms, Languages, Theory