Results 181 to 190 of about 790 (217)

How to store a triangular matrix

IEEE Transactions on Computers, 1992
The problem of storing a triangular matrix so that each row and column is stored as a vector, i.e. the locations form an arithmetic progression, is discussed. Storing rows and columns as vectors can speed up access significantly. It is shown that there is no such storage method that does not waste approximately one-half of the computer memory. >
Andrea S. LaPaugh, Richard J. Lipton, Jonathan S. Sandberg   +2 more
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On Skew Triangular Matrix Rings

Algebra Colloquium, 2015
Let R be a ring with an endomorphism σ. We show that the clean property and various Armendariz-type properties of R are inherited by the skew matrix rings S(R,n,σ) and T(R,n,σ). They allow the construction of rings with a non-zero nilpotent ideal of arbitrary index of nilpotency which inherit various interesting properties of rings.
Habibi, M., Moussavi, A., Alhevaz, A.
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Triangular Matrix Representations and Triangular Matrix Extensions

2013
In this chapter, generalized triangular matrix representations are discussed by introducing the concept of a set of left triangulating idempotents. A criterion for a ring with a complete set of triangulating idempotents to be quasi-Baer is provided.
Gary F. Birkenmeier, Jae Keol Park, S. Tariq Rizvi   +2 more
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Conditioning of the Exponential of a Block Triangular Matrix

Numerical Algorithms, 2001
A new measure of conditioning for the exponential of a block triangular matrix is proposed. It is shown that different condition numbers must be used to assess the accuracy of different algorithms for implementing diagonal Padé with scaling and squaring.
L. DIECI, PAPINI, ALESSANDRA
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Updating the Triangular Factorization of a Matrix

SIAM Journal on Matrix Analysis and Applications, 1989
A simple modification of the Bartels-Golub update [cf. \textit{R. H. Bartels} and \textit{G. H. Golub}, Commun. ACM 12, 266-268 (1969; Zbl 0181.191)] of the triangular factorization \(PB=LU\) of a given nonsingular matrix B is presented if a column of B is replaced, such that the true new factors L and U are yielded instead of their representations in ...
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On Continuous Triangularization of Matrix Functions

SIAM Journal on Mathematical Analysis, 1979
This article is concerned with the continuous triangularization of matrix functions which depend continuously on several variables. By use of an algorithm analogous to the one employed for the reduction of a $\lambda $-matrix to a diagonal form, we find a continuous similarity transformation which produces the triangularization of a given matrix.Let ...
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Fast triangularization of a symmetric tridiagonal matrix

Journal of Parallel and Distributed Computing, 1989
A simple linear systolic array is presented for triangularizing a symmetric tridiagonal matrix by Gaussian Elimination using nearest neighbor pivoting. The array consists of three cells requiring an area bounded by four simple inner product cells. The design can compute the elimination in time 2n + k1 for the simple point case and using an implicit 2*2
David J. Evans 0001, Graham M. Megson
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Triangular matrix inversion on systolic arrays

Parallel Computing, 1990
Abstract We study the systolic implementation of the algorithm which inverts a triangular matrix A of order n , by pipelining n linear systems of equation Ax h = e h , for h = 1,…, n , where e h denotes the h th vector of the canonical basis. It is known that the time complexity of the problem is T = 2 n − 1.
Basile Louka, Maurice Tchuenté
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TRIANGULAR MATRIX REPRESENTATIONS OF SEMIPRIMARY RINGS

Journal of Algebra and Its Applications, 2002
In this paper we characterize internally a TSA ring (i.e. a generalized triangular matrix ring with simple Artinian rings on the diagonal) in terms of its prime ideals. Also we show that the class of semiprimary quasi-Baer rings is a proper subclass of the class of TSA rings.
Birkenmeier, Gary F., Kim, Jin Yong, Park, Jae Keol   +2 more
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ON THE SPECTRA OF NONNEGATIVE TRIANGULAR MATRIX TRANSFORMATIONS

Analysis, 1983
Let \(A=(A_{nk})\) be a triangular matrix transformation with the spectrum \(\sigma\) (A). Suppose that \(S=\{A_{nn}:\quad n\geq 0\}\) and \(\gamma =\underline{\lim} A_{nn}.\) For 0\(\leq a\leq 1\) let \(D_ a\) denote the disc \(\{z:\quad| z-1/(2-a)|\leq (1-a)/(2-a)\}.\) Theorem 1 gives necessary and sufficient conditions in order that A is equivalent ...
Avdispahić, M., Tanović-Miller, N.
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