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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.  ...  Handling of m x n matrices (m > n) requires a QR-factorization as a preprocessing step where again the systolic array is used. The algorithm requires O(m + nlogn) units of time. W.  ... 

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

1988 Mathematical Reviews  
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.  ...  Vectorized algorithms and systolic arrays for Toeplitz systems of equations. Soviet J. Numer. Anal. Math. Modelling 2 (1987), no. 2, 99-111.  ... 

Parallel solution of certain Toeplitz least-squares problems

A. Bojańczyk, R.P. Brent
1986 Linear Algebra and its Applications  
The sequential algorithm takes time 0( n"); the systolic algorithm takes time O(n) using a linear systolic array of O(n) cells.  ...  We describe a systolic algorithm for solving a Toeplitz least-squares problem of special form.  ...  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

Page 7763 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
This algorithm requires 4n 65F Numerical linear algebra 97m:65062 time steps to solve the linear system. The elapsed time within a time step is independent of the problem size n.  ...  An important consideration is that the pivot row can be changed during the execution of our systolic algorithm. The computational model consists of linear systolic arrays.  ... 

Page 5116 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Bohme, A linear systolic array for the adaptive MVDR beam- former (705-711); Zahari Zlatev, Solving band systems of linear equations by iterative methods on vector machines (713-725).  ...  Audone, Utilization of the matrix pencil to extract poles of a linear time-invariant system (581-585); Tapan K.  ... 

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

1988 Mathematical Reviews  
Upon discretizing the integral equation, the authors arrive at a linear system of equations, which is solved iter- atively by the Gauss-Seidel method.  ...  It is shown that the time complexity of this systolic algorithm is O(n + p) and that the total storage is O(n) words.  ... 

Page 1159 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
, algorithms for band matrices, vector algorithms and systolic arrays.  ...  The second chap- ter, “Computational algorithms”, contains the following sections: inversion of Toeplitz matrices, solution of linear equations, meth- ods for block Toeplitz matrices, ill-posed problems  ... 

Page 6361 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
For OROW-PRAMs we show that our parallel algorithms are work-optimal.” 97j:68042 68Q22 68Q35 OkéSa, Gabriel Time-minimal linear systolic arrays for the Toeplitz system of linear equations.  ...  Summary: “In this paper, two linear systolic arrays for the so- lution of general, strongly regular Toeplitz systems of equations are presented.  ... 

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

Fast orthogonalization algorithm and parallel architecture for AR spectral estimation based on forward-backward linear prediction

K.J. Ray Liu, S.F. Hsieh
1993 IEEE Transactions on Signal Processing  
The fast algorithm can also be easily implemented onto a linear systolic array. The number of time steps required is further reduced to 2m + 5n -4 by using the parallel implementation.  ...  However, without exploiting the special structure of the FBLP matrix, the QR decomposition (QRD) of the FBLP matrix has the computational complexity on the order of 2(6mn ) n 2 / 3 + O(n2) for a 2m x n  ...  This algorithm can also be implemented onto a fully pipelined multiphase linear systolic array. The number of time steps required is further reduced to 2m + 5 -4 for the parallel implementation.  ... 
doi:10.1109/78.205755 fatcat:2j4nu4epzjbi7aqlwrzprzsimq

Systolic implementation of the lattice algorithm for least squares linear prediction problems

A.W. Bojanczyk
1986 Linear Algebra and its Applications  
We present a linear systolic array of O(n) cells that solves the least squares linear prediction problem in time O(n) via an algorithm based on the so-called lattice algorithm.  ...  The total storage required is O(n) words, i.e., only a constant number of words are needed at each cell.  ...  ,xP,xP+r] and the vector xi: or, by forming the normal equations, as the problem of solving the following linear system of equations for the symmetric positive-definite Toeplitz matrix X:X, and the vector  ... 
doi:10.1016/0024-3795(86)90160-6 fatcat:2czl66epdreonia5zscefgj5ia

Architectures for block Toeplitz systems

Ilias Bouras, George-Othon Glentis, Nicholas Kalouptsidis
1996 Signal Processing  
In this paper efficient VLSI architectures of highly concurrent algorithms for the solution of block linear systems with Toeplitz or near-to-Toeplitz entries are presented.  ...  The main features of the proposed scheme are the use of scalar only operations, multiplications/divisions and additions, and the local communication which enables the development of wavefront array architecture  ...  Eq. (5) determines the optimal FIR filter in the MSE sense. The pertinent filter is obtained as the solution of a block linear system of equations with Toeplitz matrices as entries.  ... 
doi:10.1016/0165-1684(96)00041-2 fatcat:gvlnfusymjgjha3jnkpvpglube

An inverse factorization algorithm for linear prediction

James Nagy, Robert J. Plemmons
1992 Linear Algebra and its Applications  
We also provide a linear systolic array for solving these problems.  ...  need for solving triangular systems.  ...  The numbers of time steps for our systolic array are given by: (1) n + 3p, for the initialization, and (2) &$ + $a for the main loop.  ... 
doi:10.1016/0024-3795(92)90025-6 fatcat:ji6qwm3gbrcyhbzgn2zx6uswdy

Book reports

1992 Computers and Mathematics with Applications  
Systolic arrays for group explicit methods for solving first order hyperbolic equations. V. Solution of linear systems. 14. Systolic block LU decompositions. 15.  ...  Introduction to systems of linear equations (linear systems) and related properties of matrices. 2. I~roduction to linear progrAmmln~. 3. F_Aementary properties of the feasible set for an LP. 4.  ...  Topology, computer science, ~ the n~then~tlcs of convergence. 2. The soundness and completeness of axioms for CSP processes. 3. Classifying unbounded nondetermlnlsm in CSP. 4.  ... 
doi:10.1016/0898-1221(92)90024-c fatcat:hnukgvg2rrdqxap57mmbikmjju

Design and Chip Implementation of A SMI/MVDR Dual-mode Beamformer for Wireless MIMO Communication Systems

Kuan-Ting Chen, Yin-Tsung Hwang, Cheng-Yi Huang
2020 IEEE Access  
A systolic array based mapping procedure converts the two beamforming algorithms to a unified hardware accelerator design with 80% shared circuitry.  ...  Multiple-Output (MIMO) communication systems.  ...  This is because their designs are all based on a linear systolic array structure.  ... 
doi:10.1109/access.2020.2986028 fatcat:ezanpqetfjbs5jrdm3ylytjgqe
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