Modified givens rotations for inverse updating in qr decomposition

The computational complexity comparison of these algorithms is also presented.

We survey general techniques and open problems in numerical linear algebra on parallel architectures.

The triangular part consists of two different node types: Boundary cell and Internal ce... This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants.

For a given matrix H which has d singular values larger than e, we find all rank d approximants H such that ..." This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants.

We illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Introduction An adaptive filter is defined as a self-designing system that relies for its operation on a recursive algorithm, which makes it possible for the filter to perform satisfactorily in an environment where knowledge of the relevant statistics is not available.

Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymmetric eigenvalue problem, and the singular value decomposition. Adaptive filters are classif ..." Introduction An adaptive filter is defined as a self-designing system that relies for its operation on a recursive algorithm, which makes it possible for the filter to perform satisfactorily in an environment where knowledge of the relevant statistics is not available.

In an earlier paper, an approximate SVD updating scheme has been derived as an interlacing of a QR updating on the one hand and a Jacobi-type SVD procedure on the other hand, possibly supplemented with a certain re-orthogonalization scheme.

AMS(MOS) : 65F15, 65F25, CR: G.1.3 Running Head : SVD Updating 1 Introduction The problem of continuously updating matrix decompositions as new rows are appended, frequently occurs in signal processing applications. Furthermore it is shown how a square root free implementation is obtained by combining modified Givens rotations with approximate SVD schemes.

Typical examples are adaptive beamforming, direction finding, spectral analysis, pattern recognition, etc. In section 2, the updating algorithm is briefly review... This paper provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines.

Furthermore it is shown how a square root free implementation is obtained by combining modified Givens rotations with approximate SVD schemes.

Keywords : Singular Value Decomposition, Parallel Algorithms, Recursive Least Squares. this paper, we show how this updating algorithm can be mapped onto a systolic array with O(n 2 ) parallelism, resulting in an O(n 0 ) throughput (much like it is the case for merely QR updating, see =-=[5]-=-).

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