This paper presents a new efficient recursive algorithm for judging the positive-definiteness of a matrix. With this algorithm, both a simpler computation process and a decreased memory requirement can be obtained.doi:10.1080/00207178808906040CHUNG-LI JIANG...
Define definiteness. definiteness synonyms, definiteness pronunciation, definiteness translation, English dictionary definition of definiteness. adj. 1. a. Clearly defined; explicitly precise: a definite statement of the terms of the will. See Synonyms a
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite...
I'm asking because of the thread in the first link that Ameer posted way earlier in this thread that shows that the chol function may not be reliable in determining if a matrix is SPD (repeating the link here for easy access):https://www.math...
摘要: It is shown how the Schur complement theory can be used for the derivation of criteria for the definiteness (or semidefiniteness) of the restriction of a quadratic form to the null space of a matrix.关键词: CiteSeerX citations and Crouzeix J.-P Definiteness and semidefiniteness of ...
A definiteness test for a Hankel matrixR={r i+j } =0 and its lower submatrixS={r i+j+1 } =0 is given. The test allows a description of all extensions ofR w
GCD type matrix Inertia Positive definiteness Matrix norm Arithmetical convolution Asymptotic formula 1. Introduction Let S={x1,x2,…,xn} be a set of distinct positive integers, and let f be an arithmetical function (function from the positive integers into the reals). The GCD matrix (S)f ...
Further, definiteness can be checked using the determinants of the sub-matrices \(\mx{A}_{[ij,kl]}\) as follows: given a matrix \[ \mx{A} = \begin{bmatrix} \begin{tikzpicture}[ outer sep = 2pt, inner sep = 2pt, ] \matrix (m) [ matrix of nodes, row sep = 3pt, column ...
Thus, a positive definite matrix \(\varvec{V}\) is also positive semi-definite; however, the converse of the statement is not true. In a portfolio context, suppose that \(\varvec{V}\) is the covariance matrix of security returns and \(\varvec{x}\) is a portfolio weight vector. ...
Next, the matrix of simulated bulk responses, [Y’], including 4 different bulk responses for 18 samples, is created. This matrix is used to map relationships between DEM variables, X, and simulated bulk responses, Y’. Details of F(X) are presented in Table 9, including coefficients of ...