We present very efficient arithmetic circuits for the computation of the determinants and inverse of band matrices and for interpolation and polynomial arithmetic over arbitrary ground fields. For input size n the circuits for band matrix inversion (for constant band width) over infinite fields, and the circuits for polynomial arithmetic over arbitrary fields, have optimal depth 0(log n) and polynomial size. The algorithm for band matrix inversion is based on an extension of the method of modification (from numerical analysis) which includes a formula for the determinant of a modified matrix.

Very Fast Parallel Matrix and Polynomial Arithmetic

A new method for the solution of pentadiagonal systems of linear equations is presented. The method is a generalization of ordinary odd-even elimination used for tridiagonal systems. Using n processors, an n X n pentadiagonal system can be solved using the new method (generalized odd-even elimination) in time proportional to log2n.

Parallel solution of pentadiagonal systems using generalized odd-even elimination

Phase Noise in Multi-carrier Systems

Parallel solution of block tridiagonal linear-systems

Pent: A periodic pentadiagonal systems solver

We illustrate some 0 (logn) parallel algorithms for invertingn×n tridiagonal and pentadiagonal matrices. Also, an 0(logn) parallel algorithm is proposed to computer th order linear recurrences and the determinant ofr-band Hessenberg matrices.

On some parallel algorithms for inverting tridiagonal and pentadiagonal matrices

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On some parallel algorithms for inverting tridiagonal and pentadiagonal matrices