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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]

1988
*
IMA Volumes in Mathematics and its Applications
*

The most popular method

doi:10.1007/978-1-4684-6357-6_7
fatcat:2i7qk7mjkrgatny5lrh7gefniq
*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 ...##
###
Parallel solution of certain Toeplitz least-squares problems

1986
*
Linear Algebra and its Applications
*

We describe

doi:10.1016/0024-3795(86)90161-8
fatcat:xcmcv5yi7jgbzavblor54ww7ci
*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),... ...##
###
A systolic array for the regularization of III-conditioned least-squares problems with triangular Toeplitz matrix

1986
*
Linear Algebra and its Applications
*

The

doi:10.1016/0024-3795(86)90165-5
fatcat:x5amqy7jxnd2hawmh62hpptwwm
*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. ...##
###
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]

2010
*
arXiv
*
pre-print

We show how n * n

arXiv:1004.3716v1
fatcat:oq36fqmkorfstgbvaub7pjmuqe
*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. ...##
###
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

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. ...

##
###
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

1986
*
Linear Algebra and its Applications
*

An algorithm based on hyperbolic rotations is presented

doi:10.1016/0024-3795(86)90163-1
fatcat:wzqbdkeskbd7bgypxwfv3s5ieq
*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. ...##
###
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

1993
*
Linear Algebra and its Applications
*

This paper is concerned with the development

doi:10.1016/0024-3795(93)90322-f
fatcat:rpm2epx56rfmxan4tp4zb7ywy4
*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. ...##
###
VLSI Array processors

1985
*
IEEE ASSP Magazine
*

Example 2: Comparison

doi:10.1109/massp.1985.1163741
fatcat:dc6jsvtgabar7ffr343nhdzqiy
*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. ...##
###
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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