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Published **1984**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va .

Written in English

- Decomposition method

**Edition Notes**

Statement | Ilse C.F. Ipsen |

Series | NASA contractor report -- 172396, ICASE report -- no. 84-30 |

Contributions | Langley Research Center, Institute for Computer Applications in Science and Engineering |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL14928216M |

Linear time computation of the singular value decomposition (SVD) would be useful in many real time signal processing applications. Two algorithms for the SVD have been developed for implementation on a quadratic array of processors. A specific architecture is proposed and we demonstrate the mapping of the algorithms to the by: Singular value decomposition on processor arrays with a pipelined bus system by mapping the systolic array architecture onto a ring connected linear array due to the double sends and receives required between pairs of neighboring processors. Eberlein [11], Bischof [12] and others have proposed various modiﬁcations of this. Systolic arrays for determining the Singular Value Decomposition of a mxn, m > n, matrix A of bandwidth w are presented. After A has been reduced to bidiagonal form B by means of Givens plane rotations, the singular values of B are computed by the Golub-Reinsch iteration. The products of plane rotations form the matrices of left and right singular by: In many applications it is required to adaptively compute the singular value decomposition (SVD) of a data matrix whose size nominally increases with time. In situa- tions of high nonstationarity, the window of choice is a constant amplitude sliding window.

Singular Value Decomposition. We saw in that the eigendecomposition can be done only for square matrices. The way to go to decompose other types of matrices that can’t be decomposed with eigendecomposition is to use Singular Value Decomposition (SVD).. We will decompose $\bs{A}$ into 3 matrices (instead of two with eigendecomposition). Systolic arrays are specialized form of parallel computing, where processors connected by short wires. An example of two dimensional systolic array is given in the Figure 2 given below. Figure 2: Architecture of Systolic Array [9] The array given above takes in inputs parallel performs parallel processing and outputs the result. Systolic arrays. of the systolic array dimensions. The following sections start with the motivation for seek-ing an algorithm with strong scaling properties, and move on to general background on systolic arrays and the QR decom-position. Then the systolic array for the QR decomposition is presented and its software implementation is described. A has two sets of singular vectors (the eigenvectors of A TA and AA). There is one set of positive singular values (because A TA has the same positive eigenvalues as AA). A is often rectangular, but ATA and AAT are square, symmetric, and positive semideﬁnite. The Singular Value Decomposition (SVD) separates any matrix into simple pieces.

However, the information hidden in the data can be made explicit through singular value decomposition (SVD). SVD based signal processing is making headway and will become feasible soon, thanks to the progress in parallel computations and VLSI implementation. The book . 1 Singular Value Decomposition (SVD) The singular value decomposition of a matrix Ais the factorization of Ainto the product of three matrices A= UDVT where the columns of Uand Vare orthonormal and the matrix Dis diagonal with positive real entries. The SVD is useful in many tasks. Here we mention some examples. We shall discuss LU and QR factorizations, eigenvalue problems, and the singular value decomposition. All the work we shall describe has been done since 19 Our aim is to introduce the reader to this rapidly developing branch of numerical computation. Systolic arrays were introduced and named by Kung and Leiserson [12]. Efficient systolic array for singular value and eigenvalue decomposition. 46th Midwest Symposium on Circuits and Systems, Singular value computations on .

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