BIT Numerical Mathematics

, Volume 30, Issue 1, pp 2–16 | Cite as

A general transposition method for a matrix on auxiliary store

  • Nils Andersen
Part I Computer Science


An algorithm is developed and described for transposing a matrix larger than available working storage. If an (n×m)-matrix is stored in row-major order, and blocks ofn elements may be transferred to and from working storage at a time, the algorithm needsw=(5[m/n]+8)·n elements to be present in working storage at a time and requires [log2(2mn/w)] passages over the matrix. The algorithm is as efficient as earlier methods but needs no extra backing storage space. An algebra for mixed radix notation and a generalization of mixed radix notation is introduced for the description and verification of transposition algorithms, and earlier algorithms are briefly certified or disproved.

CR categories

E.2 F.2.1 G.4 I.1.2 


Matrix transposition mixed radix notation 


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Copyright information

© BIT Foundations 1990

Authors and Affiliations

  • Nils Andersen
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenKøbenhavn ØDenmark

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