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Page 3161 of Mathematical Reviews Vol. , Issue 88f [page]

1988 Mathematical Reviews  
A.; Tyrtyshnikov, E. E. Vectorized algorithms and systolic arrays for Toeplitz systems of equations. Soviet J. Numer. Anal. Math. Modelling 2 (1987), no. 2, 99-111.  ...  The solution of systems of order n on SIMD computers with O(n) processors requires O(n) time and O(n) storage. A systolic array is obtained for the on-line solution of Toeplitz systems.  ... 

Systolic Algorithms for the Parallel Solution of Dense Symmetric Positive-Definite Toeplitz Systems [chapter]

Ilse C. F. Ipsen
1988 IMA Volumes in Mathematics and its Applications  
The most popular method for the solution of linear systems of equations with Toeplitz coefficient matrix on a single processor is Levinson's algorithm, whose intermediate vectors form the Cholesky factor  ...  This increased exploitation of the Toeplitz structure then leads to more efficient parallel I implementations on systolic arrays.  ...  Introduction The aim of this paper is to discuss parallel methods for the solution of linear systems of equations Tx= f whose coefficient matrices T are dense symmetric positive-definite Toeplitz matrices  ... 
doi:10.1007/978-1-4684-6357-6_7 fatcat:2i7qk7mjkrgatny5lrh7gefniq

Parallel solution of certain Toeplitz least-squares problems

A. Bojańczyk, R.P. Brent
1986 Linear Algebra and its Applications  
We describe a systolic algorithm for solving a Toeplitz least-squares problem of special form.  ...  The sequential algorithm takes time 0( n"); the systolic algorithm takes time O(n) using a linear systolic array of O(n) cells.  ...  A similar observation was made by Brent and Luk [l] and exploited in a systolic algorithm for the solution of Toeplitz systems of equations. ( Cl, sl),...  ... 
doi:10.1016/0024-3795(86)90161-8 fatcat:xcmcv5yi7jgbzavblor54ww7ci

A systolic array for the regularization of III-conditioned least-squares problems with triangular Toeplitz matrix

Lars Eldén, Robert Schreiber
1986 Linear Algebra and its Applications  
The array consists of 2n processor elements (for a problem with n unknowns), connected in a linear mesh, and it computes a decomposition of the matrix in 3n time steps.  ...  This paper describes the implementation of this algorithm in a systolic array.  ...  Systolic arrays for least-squares problems like (l), but without Toeplitz structure, were described in [4] . THE ALGORITHM AND THE SYSTOLIC ARRAY 2.1.  ... 
doi:10.1016/0024-3795(86)90165-5 fatcat:x5amqy7jxnd2hawmh62hpptwwm

Page 8039 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
To achieve high performance, new systolic array designs for the algorithm shown above are implemented. A full description of the systolic array designs is given in a later section.  ...  Summary: “This paper is concerned with a new approach to pre- conditioning for large, sparse linear systems.  ... 

Some linear-time algorithms for systolic arrays [article]

Richard P. Brent, Franklin T. Luk, H. T. Kung
2010 arXiv   pre-print
We show how n * n Toeplitz systems of linear equations can be solved in time O(n) on a linear array of O(n) cells, each of which has constant memory size (independent of n).  ...  We survey some results on linear-time algorithms for systolic arrays.  ...  The work of the third author was supported in part by the Mathematical Sciences Research Centre and the Centre for Mathematical Analysis, Australian National University.  ... 
arXiv:1004.3716v1 fatcat:oq36fqmkorfstgbvaub7pjmuqe

Page 5762 of Mathematical Reviews Vol. , Issue 86m [page]

1986 Mathematical Reviews  
Author summary: “A fast algorithm for the solution of a Toeplitz system of equations is presented. The algorithm requires order N(log N)? computations, where N is the number of equations.  ...  Kumar, Rajendra (1-CASLB) 86m:65035 A fast algorithm for solving a Toeplitz system of equations. IEEE Trans. Acoust. Speech Signal Process. 33 (1985), no. 1, 254-267.  ... 

Old And New Algorithms For Toeplitz Systems

Richard P. Brent, Franklin T. Luk
1988 Advanced Algorithms and Architectures for Signal Processing III  
Toeplitz linear systems and Toeplitz least squares problems commonly arise in digital signal processing.  ...  We concentrate our attention on algorithms which can be implemented efficiently on a variety of parallel machines (including pipelined vector processors and systolic arrays).  ...  elements in a linear array of n + 1 systolic cells.  ... 
doi:10.1117/12.948485 fatcat:a335rtof3vfdtlvmmk35gzi5yi

Page 1047 of Mathematical Reviews Vol. , Issue 88b [page]

1988 Mathematical Reviews  
Then a systolic implementation of this modified lattice algorithm is presented. It is based on a one-dimensional linear array of pro- grammable cells.  ...  Upon discretizing the integral equation, the authors arrive at a linear system of equations, which is solved iter- atively by the Gauss-Seidel method.  ... 

Parallel solution of symmetric positive definite systems with hyperbolic rotations

Jean-Marc Delosme, Ilse C.F. Ipsen
1986 Linear Algebra and its Applications  
An algorithm based on hyperbolic rotations is presented for the solution of linear systems of equations Ax = b, with symmetric positive definite coefficient matrix A.  ...  This method can be simplified and formulated without square roots if A is also Toeplitz; a systolic (VLSI) architecture implementing the resulting recurrence equations is more efficient than previously  ...  We are grateful to Professor Martin Morf for having suggested the ansatz presented in this paper.  ... 
doi:10.1016/0024-3795(86)90163-1 fatcat:wzqbdkeskbd7bgypxwfv3s5ieq

Page 5437 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
The aim of the paper is to extend the theory for more gen- eral systems of recurrence equations.  ...  This paper is devoted to the development of systematic methods for the automatic synthesis of systolic arrays. Systolic arrays are regular networks of tightly coupled processors with limited storage.  ... 

Efficient algorithms for the solution of block linear systems with Toeplitz entries

George-Othon Glentis, Nicholas Kalouptsidis
1993 Linear Algebra and its Applications  
This paper is concerned with the development of fast solvers for block linear systems with Toeplitz entries. Two algorithms are described.  ...  The first utilizes block permutations to unravel the nesting structure of the associated matrix. The second has a block Schur type format and features highly parallel potential.  ...  Conclusion In this paper, two fast, order recursive algorithms for the solution of block linear systems with Toeplitz entries have been presented.  ... 
doi:10.1016/0024-3795(93)90322-f fatcat:rpm2epx56rfmxan4tp4zb7ywy4

VLSI Array processors

S. Kung
1985 IEEE ASSP Magazine  
Example 2: Comparison of Linear System Solvers It is well known that there are three major numerical algorithms for solving a linear system of equations; namely, the LU decomposition, the Householder QR  ...  Parallel array algorithm design is a new area of, research study that has profited from the theory of signals and systems and has been influenced by linear algebraic numerical methods.  ... 
doi:10.1109/massp.1985.1163741 fatcat:dc6jsvtgabar7ffr343nhdzqiy

Page 45 of Mathematical Reviews Vol. , Issue 90G [page]

1990 Mathematical Reviews  
A parallel pipeline technique is proposed for computing sequences of k-point DFTs, for every k < n, on a systolic array.” 90g:65033 65F05 01A65 65-03 0C27 George, Alan (1-TN-C); Liu, Joseph W.  ...  Summary: “We briefly describe the generalized Schur algorithm for the superfast solution of positive definite Toeplitz systems of equa- tions and its relationship with Schur’s algorithm and the Szegé re  ... 

Page 3879 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
This system is solved by means of fast algorithms which are realized on linear systolic arrays.” 97f:68058 68Q22 12Y05 13P99 65Y05 65Y20 68Q40 Pan, Victor Y. (1-CUNY7; Bronx, NY) A new approach to parallel  ...  (PL-SZTU; Szczecin) Solution of Boolean differential equations on systolic arrays. (Russian. English and Ukrainian summaries) Kibernet. Sistem.  ... 
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