Results 261 to 270 of about 120,420 (290)

On the Inversion of Ill-Conditioned Matrices

IEEE Transactions on Reliability, 1980
A recent paper presented a modification of the Gauss-Jordan method for inverting a matrix which avoids loss of accuracy due to a type of ill-conditioning which leads to subtractive cancellation. This paper shows the relationship between the standard and modified techniques, and why and when the latter is effective.
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Conditional negativity of anti-Loewner matrices

Linear and Multilinear Algebra, 2012
Let f be a positive, continuously differentiable function on (0, ∞). We consider matrices K f of the form We show that for such a function f with f(0) = f ′(0) = 0, all K f are conditionally negative definite if and only if all are positive semidefinite (p.s.d.), and give the integral representation of f.
Chikara Hidaka, Takashi Sano
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On the Condition of Symmetric Quasi-Definite Matrices

SIAM Journal on Matrix Analysis and Applications, 2000
Powerful algorithms and efficient data structures are developed for solving sparse positive definite systems of linear equations. A method of solving sparse (non-symmetric) systems is to first augment it to make it symmetric quasi-definite and then use available algorithms for symmetric systems.
George, Alan, Ikramov, Kh.
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Conditioning of Pseudospectral Matrices for Certain Domain Decompositions

Journal of Scientific Computing, 1999
The authors examine the conditioning of systems resulting from conforming Chebyshev spectral approximations in nonconforming domain decompositions in rectangular domains. The resulting matrices are large, relatively sparse and have block structures. When solving fourth order systems, the resulting matrices suffer from poor conditioning.
Karageorghis, Andreas, Paprzycki, Marcin
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On the spectral condition of rectangular vandermonde matrices

Calcolo, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FASINO, Dario, INGLESE G.
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Conditioning of Collocation Matrices and Discrete Green’s Functions

SIAM Journal on Numerical Analysis, 1986
The boundary value problem \(Lu(x)=u^{(m)}(x)-\sum^{m}_{i=1}C_ i(x)u^{(i-1)}(x)=f(x)\), \(x\in [a,b]\); \(B_ aZ(u(a))+B_ b(u(b))=\beta,\) \(B_ a,B_ b\in R^{m\times m}\), \(Z(u(x))=(u(x),u'(x),...,u^{(m-1)}(x))^ T\) is considered. The stability and related conditioning of spline collocation matrices is analysed. Hermite-type and B-spline bases are used.
Paine, John, Russell, Robert D.
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Coherence of randomly pre-conditioned matrices

2017 Indian Control Conference (ICC), 2017
In many applications of compressed sensing, coherence of the matrix A plays an important role in theoretical guarantees for obtaining sparse solutions to linear system of equations, y = Ax. For a given matrix G with trivial right null space, the system Gy = GAx is equivalent.
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Reducibility Condition of a Class of Rational Function Matrices

SIAM Journal on Matrix Analysis and Applications, 1994
A reducibility criterion for a class of rational function matrices is obtained. The coefficient matrix of any resistor-inductor-capacitor (RLC) network is such a rational function matrix. Hence the reducibility criterion can be applied to the controllability and observability of RLC networks over the field \(F_ \xi\) of all rational functions with real
Lu, Kai Sheng, Wei, Jia Ning
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The condition of gram matrices and related problems

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978
SynopsisIt has been known for some time that certain least-squares problems are “ill-conditioned”, and that it is therefore difficult to compute an accurate solution. The degree of ill-conditioning depends on the basis chosen for the subspace in which it is desired to find an approximation. This paper characterizes the degree of ill-conditioning, for a
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Estimating Extremal Eigenvalues and Condition Numbers of Matrices

SIAM Journal on Numerical Analysis, 1983
A method for estimating the largest (or smallest) eigenvalue of a real positive definite matrix is given. It uses a probabilistic algorithm to compute an estimate which will line within a prescribed distance from the true value. It is a non-iterative method and its execution time can be estimated ''a priori''.
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