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Diagonal dominance, Schur complements and some classes of H-matrices and P-matrices
Advances in Computational Mathematics, 2010\(SDD_1\)-matrices are introduced as a special class of \(H\)-matrices which generalize strict diagonal dominance by rows. One result of the theoretical investigations is an algorithm of complexity \(O(n^2)\) for checking whether a square matrix belongs to the class \(SDD_1\) or not.
J M Pena, Pena Juan Manuel
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A note on a characterization of P-matrices
Mathematical Programming, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. R. Mohan, R. Sridhar 0002
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A Recursive Test for P-Matrices
BIT Numerical Mathematics, 2000The paper is devoted to the problem of testing whether a given square matrix is a P-matrix, that is all its principle minors are positiv. It is known that the comlexity of a direct approach (direct computation of all principle minors) or of an LU factorization method is \(O(2^n n^3)\).
Tsatsomeros, Michael J., Li, Lei
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Linear and Multilinear Algebra, 1998
Several possibilities to generalize P-matrices to block form are discussed. Unfortunately certain equivalences holding for P-matrices do not carry over to the block case. We opt for one such generalization calling it block P-matrices. It has the most analogies to the usual P-matrices.
Elsner, Ludwig, Szulc, Tomasz
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Several possibilities to generalize P-matrices to block form are discussed. Unfortunately certain equivalences holding for P-matrices do not carry over to the block case. We opt for one such generalization calling it block P-matrices. It has the most analogies to the usual P-matrices.
Elsner, Ludwig, Szulc, Tomasz
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SIAM Journal on Matrix Analysis and Applications, 1996
Summary: A characterization of interval \(P\)-matrices is given. The result implies that a symmetric interval matrix is a \(P\)-matrix if and only if it is positive definite (although nonsymmetric matrices may be involved). As a consequence it is proved that the problem of checking whether a symmetric interval matrix is a \(P\)-matrix is NP-hard.
Jiri Rohn, Georg Rex
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Summary: A characterization of interval \(P\)-matrices is given. The result implies that a symmetric interval matrix is a \(P\)-matrix if and only if it is positive definite (although nonsymmetric matrices may be involved). As a consequence it is proved that the problem of checking whether a symmetric interval matrix is a \(P\)-matrix is NP-hard.
Jiri Rohn, Georg Rex
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Convex sets of nonsingular and P:–Matrices
Linear and Multilinear Algebra, 1995We show that the set r(A,B) (resp. c(A,B)) of square matrices whose rows (resp.
Charles R. Johnson +1 more
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STOPBANDS, COM PARAMETERS, AND P MATRICES
2006 Multiconference on Electronics and Photonics, 2006Dispersion curves for 128 Lithium Niobate, YZ Lithium Niobate, 42 Lithium Tantalate, STX Quartz, STX+25 Quartz, ATX Quartz, and LGS crystals are calculated with modified Hasimoto's program. Dependences of obtained COM parameters on the electrode width and thickness are approximated by polynomials and used for calculations of admittance of transducer ...
Valentine Cherednick +1 more
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