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positive definite?
, 2011
"... Let L be a positive definite bilinear functional, then the Uvarov transformation of L is given by U(p, q) = L(p, q) + m p(α)q ( α −1) + m p ( α −1) q(α) where α > 1, m ∈ C. In this paper we analyze conditions on m for U to be positive definite in the linear space of polynomials of degree less ..."
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Let L be a positive definite bilinear functional, then the Uvarov transformation of L is given by U(p, q) = L(p, q) + m p(α)q ( α −1) + m p ( α −1) q(α) where α > 1, m ∈ C. In this paper we analyze conditions on m for U to be positive definite in the linear space of polynomials of degree less
POSITIVE DEFINITENESS OF TRIDIAGONAL MATRICES
, 1998
"... Positive definiteness of tridiagonal matrices via the numerical range ..."
Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions
 CONSTRUCTIVE APPROXIMATION
, 1986
"... Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke. ..."
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Cited by 360 (3 self)
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Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.
Metric spaces and positive definite functions
 Transactions of the American Mathematical Society
, 1938
"... generally EmP the pseudoeuclidean space of m real variables with the distance function p> o. As p ~ 00 we get the space E = with the distance function maXi=l,...,m IXi xl I. ..."
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Cited by 194 (0 self)
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generally EmP the pseudoeuclidean space of m real variables with the distance function p> o. As p ~ 00 we get the space E = with the distance function maXi=l,...,m IXi xl I.
Positive Definite Solutions
"... Abstract: The matrix equation X − A∗√X −1A = I in this paper is studied. There is an iterative method for obtaining of a positive definite solution of this equation. Sufficient conditions for existence of positive definite solutions are proved. Results of numerical expiriments are given. ..."
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Abstract: The matrix equation X − A∗√X −1A = I in this paper is studied. There is an iterative method for obtaining of a positive definite solution of this equation. Sufficient conditions for existence of positive definite solutions are proved. Results of numerical expiriments are given.
On positivedefinite functions
 Proc. London Math. Soc
, 1956
"... 1. LET p(x) be a real or complexvalued function of x = (x L ix 2)...,x m), a point of R m; then p(x) is 'positivedefinite ' if for all finite sets x^, and all ..."
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Cited by 8 (0 self)
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1. LET p(x) be a real or complexvalued function of x = (x L ix 2)...,x m), a point of R m; then p(x) is 'positivedefinite ' if for all finite sets x^, and all
Positive definite completions of partial Hermitian matrices
 LINEAR ALG. ITS APPLIC
, 1984
"... The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of ..."
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Cited by 126 (9 self)
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The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph
Extending positive definiteness
, 906
"... Abstract. The main result of the paper gives criteria for extendibility of sesquilinear formvalued mappings defined on symmetric subsets of ∗semigroups to positive definite ones. By specifying this we obtain new solutions of: • the truncated complex moment problem, • the truncated multidimensional ..."
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Cited by 8 (0 self)
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Abstract. The main result of the paper gives criteria for extendibility of sesquilinear formvalued mappings defined on symmetric subsets of ∗semigroups to positive definite ones. By specifying this we obtain new solutions of: • the truncated complex moment problem, • the truncated
COMPUTATIONAL GEOMETRY OF POSITIVE DEFINITENESS
"... Abstract. In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as that of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results i ..."
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Abstract. In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as that of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results
Symmetric Positive Definite Systems
, 2008
"... Use datadependent linear function space P f (x) = N∑ cjΦ(x, x j), j=1 x ∈ R s Here Φ: R s × R s → R is strictly positive definite (reproducing) kernel ..."
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Use datadependent linear function space P f (x) = N∑ cjΦ(x, x j), j=1 x ∈ R s Here Φ: R s × R s → R is strictly positive definite (reproducing) kernel
Results 1  10
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2,194,735