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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

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),... ...

##
###
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

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. ...

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

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. ...

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

1986
*
Linear Algebra and its Applications
*

We present a

doi:10.1016/0024-3795(86)90160-6
fatcat:2czl66epdreonia5zscefgj5ia
*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 ...##
###
Architectures for block Toeplitz systems

1996
*
Signal Processing
*

In this paper efficient VLSI architectures

doi:10.1016/0165-1684(96)00041-2
fatcat:gvlnfusymjgjha3jnkpvpglube
*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. ...##
###
An inverse factorization algorithm for linear prediction

1992
*
Linear Algebra and its Applications
*

We also provide a

doi:10.1016/0024-3795(92)90025-6
fatcat:ji6qwm3gbrcyhbzgn2zx6uswdy
*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. ...##
###
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. ...

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

2020
*
IEEE Access
*

A

doi:10.1109/access.2020.2986028
fatcat:ezanpqetfjbs5jrdm3ylytjgqe
*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. ...
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