2-Norm Error Bounds and Estimates for Lanczos Approximations to Linear Systems and Rational Matrix Functions

A. Frommer; K. Kahl; Th. Lippert; H. Rittich

doi:10.1137/110859749

2-Norm Error Bounds and Estimates for Lanczos Approximations to Linear Systems and Rational Matrix Functions

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/110859749 ◽

2013 ◽

Vol 34 (3) ◽

pp. 1046-1065 ◽

Cited By ~ 5

Author(s):

A. Frommer ◽

K. Kahl ◽

Th. Lippert ◽

H. Rittich

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Matrix Functions ◽

Rational Matrix ◽

Norm Error

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Spectral properties of rational matrix functions with nonnegative realizations

Linear Algebra and its Applications ◽

10.1016/s0024-3795(97)10034-9 ◽

1998 ◽

Vol 275-276 ◽

pp. 189-200 ◽

Cited By ~ 4

Author(s):

K.-H. Förster ◽

B. Nagy

Keyword(s):

Spectral Properties ◽

Matrix Functions ◽

Rational Matrix

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J-unitary rational matrix functions

A State Space Approach to Canonical Factorization with Applications ◽

10.1007/978-3-7643-8753-2_18 ◽

2010 ◽

pp. 313-345

Author(s):

Harm Bart ◽

Marinus A. Kaashoek ◽

André C. M. Ran

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Realization and Factorization for Rational Matrix Functions with Symmetries

Extension and Interpolation of Linear Operators and Matrix Functions ◽

10.1007/978-3-0348-7701-5_1 ◽

1990 ◽

pp. 1-60 ◽

Cited By ~ 1

Author(s):

Daniel Alpay ◽

Joseph A. Ball ◽

Israel Gohberg ◽

Leiba Rodman

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Conquer Step and Eigenproblem for Rational Matrix Functions

Separable Type Representations of Matrices and Fast Algorithms - Operator Theory: Advances and Applications ◽

10.1007/978-3-0348-0612-1_6 ◽

2013 ◽

pp. 95-101

Author(s):

Yuli Eidelman ◽

Israel Gohberg ◽

Iulian Haimovici

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Interpolation Problems for Rational Matrix Functions with Incomplete Data and Wiener-Hopf Factorization

Operator Theory: Advances and Applications - Topics in Interpolation Theory of Rational Matrix-valued Functions ◽

10.1007/978-3-0348-5469-6_2 ◽

1988 ◽

pp. 73-108 ◽

Cited By ~ 5

Author(s):

I. Gohberg ◽

M. A. Kaashoek ◽

A. C. M. Ran

Keyword(s):

Incomplete Data ◽

Matrix Functions ◽

Rational Matrix ◽

Interpolation Problems

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Coisometically Valued Rational Matrix Functions

Operator Theory and Boundary Eigenvalue Problems ◽

10.1007/978-3-0348-9106-6_1 ◽

1995 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Daniel Alpay ◽

Marek Rakowski

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Regular Rational Matrix Functions with Prescribed Pole and Zero Structure

Operator Theory: Advances and Applications - Topics in Interpolation Theory of Rational Matrix-valued Functions ◽

10.1007/978-3-0348-5469-6_3 ◽

1988 ◽

pp. 109-122 ◽

Cited By ~ 13

Author(s):

I. Gohberg ◽

M. A. Kaashoek

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Schur Decomposition Methods for the Computation of Rational Matrix Functions

Computational Science – ICCS 2006 - Lecture Notes in Computer Science ◽

10.1007/11758549_96 ◽

2006 ◽

pp. 708-715 ◽

Cited By ~ 1

Author(s):

T. Politi ◽

M. Popolizio

Keyword(s):

Decomposition Methods ◽

Matrix Functions ◽

Rational Matrix ◽

Schur Decomposition

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7. Rational Matrix Functions

Invariant Subspaces of Matrices with Applications ◽

10.1137/1.9780898719093.ch7 ◽

2006 ◽

pp. 212-261

Keyword(s):

Matrix Functions ◽

Rational Matrix

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Verified Error Bounds for Linear Systems Through the Lanczos Process

Developments in Reliable Computing ◽

10.1007/978-94-017-1247-7_20 ◽

1999 ◽

pp. 255-267

Author(s):

Andreas Frommer ◽

Andre Weinberg

Keyword(s):

Linear Systems ◽

Error Bounds ◽

Lanczos Process

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