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Complex variable boundary integral equations for perforated infinite planes

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2001年第3期25卷 191-202页

作者： Helsing, J Jonsson, A Royal Inst Technol Dept Solid Mech & NADA SE-10044 Stockholm Sweden

A fast and stable numerical algorithm is presented for the elastostatic problem of a linearly elastic plane with holes, loaded at infinity. The holes are free of stress. The algorithm is based on an integral equation which is intended as an alternative to the classic Sherman-Lauricella equation. The new scheme is argued to be both simpler and more reliable than schemes based on the Sherman-Lauricella equation. Improvements include simpler geometrical description, simpler relationships between mathematical and physical quantities, simpler extension to problems involving also inclusions and cracks, and more stable numerical convergence. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： linear elasticity holes integral equation of Fredholm type fast multipole method Sherman-Lauricella equation effective elastic moduli stress concentration factor numerical methods stable algorithms

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A well-conditioned and efficient Levin method for highly oscillatory integrals with compactly supported radial basis functions

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2021年 131卷 51-63页

作者： Khan, Suliman Zaman, Sakhi Arshad, Muhammad Kang, Hongchao Shah, Hasrat Hussain Issakhov, Alibek Cent South Univ Sch Math & Stat Changsha 410083 Hunan Peoples R China Univ Engn & Technol Fac Architecture Allied Sci & Humanities Peshawar Pakistan Abbottabad Univ Sci & Technol Dept Math Abbottabad Pakistan Hangzhou Dianzi Univ Sch Sci Dept Math Hangzhou 310018 Zhejiang Peoples R China Balochistan Univ Informat Technol Engn & Manageme Dept Math Sci Quetta Pakistan Al Farabi Kazakh Natl Univ Dept Math & Comp Modelling Alma Ata 050040 Kazakhstan Kazakh British Tech Univ Dept Math & Cybernet Alma Ata 050000 Kazakhstan

Highly oscillatory integrals are frequently involved in applied problems, particularly for large-scale data and high frequencies. Levin method with global radial basis functions was implemented for numerical evaluation of these integrals in the literature. However, when the frequency is large or nodal points are increased, the Levin method with global radial basis functions faces several issues such as large condition number of the interpolation matrix and computationally inefficiency of the method, etc. In this paper, the Levin method with compactly supported radial basis functions is proposed to handle deficiencies of the method. In addition, theoretical error bounds and stability analysis of the proposed methods are performed. Several numerical examples are included to verify the accuracy, efficiency, and well-conditioned behavior of the proposed methods.

关键词： Highly oscillatory integrals Compactly supported radial basis functions stable algorithms Levin method Hybrid functions

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A regularization algorithm for matrices of bilinear and sesquilinear forms

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LINEAR ALGEBRA AND ITS APPLICATIONS 2006年第2-3期412卷 380-395页

作者： Horn, RA Sergeichuk, VV Univ Utah Dept Math Salt Lake City UT 84112 USA Inst Math Kiev Ukraine

Over a field or skew field F with an involution a -> (a) over tilde (possibly the identity involution), each singular square matrix A is *congruent to a direct sum S*AS = B circle plus J(n1) circle plus ... circle plus 1 <= n(1) <= (...) <= n(p), in which S is nonsingular and S* = (S) over tilde (T);B is nonsingular and is determined by A up to *congruence;and the n(i) x n(i) singular Jordan blocks J(ni) and their multiplicities are uniquely determined by A. We give a regularization algorithm that needs only elementary row operations to construct such a decomposition. If F = C (respectively, F = R), we exhibit a regularization algorithm that uses only unitary (respectively, real orthogonal) transformations and a reduced form that can be achieved via a unitary *congruence or congruence (respectively, a real orthogonal congruence). The selfadjoint matrix pencil A + lambda A* is decomposed by our regularization algorithm into the direct sum S*(A + lambda A*)S = (B + lambda B*) circle plus (J(n1) + lambda J(n1)*) circle plus (...) circle plus (J(np) + lambda J(np)*) with selfadjoint summands. (c) 2005 Elsevier Inc. All rights reserved.

关键词： 15A63 15A21 15A22 Canonical matrices Bilinear forms Matrix pencils stable algorithms

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Computation of canonical matrices for chains and cycles of linear mappings

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LINEAR ALGEBRA AND ITS APPLICATIONS 2004年第0期376卷 235-263页

作者： Sergeichuk, VV Natl Acad Sci Inst Math Kiev Ukraine

Van Dooren [Linear Algebra Appl. 27 (1979) 103] constructed an algorithm for the computation of all irregular summands in Kronecker's canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary transformations. We construct a unitary algorithm for computation of the canonical form of the matrices of a chain of linear mappings V-1 - V-2 - (...) -V-t and extend Van Dooren's algorithm to the matrices of a cycle of linear mappings V-1 - V-2 -(...)- V-t where all V-i are complex vector spaces and each line denotes --> or <--. (C) 2003 Elsevier Inc. All rights reserved.

关键词： canonical forms pencils of matrices unitary transformations stable algorithms

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Approximation of oscillatory Bessel integral transforms

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MATHEMATICS AND COMPUTERS IN SIMULATION 2023年第1期208卷 727-744页

作者： Khan, Suliman Zaman, Sakhi Arshad, Muhammad Alhazmi, Sharifah E. Khan, Feroz Park, Jongee King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Intelligent Mfg & Robot Dhahran 31261 Saudi Arabia Univ Engn & Technol Fac Architecture Allied Sci & Humanities Peshawar Pakistan Abbottabad Univ Sci & Technol Dept Math Abbottabad Pakistan Umm Al Qura Univ Al Qunfudah Univ Coll Math Dept Mecca 2438 Saudi Arabia Hitec Univ Taxila Punjab Pakistan Atilim Univ Dept Met & Mat Engn TR-06836 Ankara Turkiye

The numerical treatment of oscillatory integrals is a demanding problem in applied sciences, particularly for large-scale problems. The main concern of this work is on the approximation of oscillatory integrals having Bessel-type kernels with high frequency and large interpolation points. For this purpose, a modified meshless method with compactly supported radial basis functions is implemented in the Levin formulation. The method associates a sparse system matrix even for high frequency values and large data points, and approximates the integrals accurately. The method is efficient and stable than its counterpart methods. Error bounds are derived theoretically and verified with several numerical experiments.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Highly oscillatory Bessel integral transforms Compactly supported radial basis functions stable algorithms Levin method Hybrid functions

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Reliable solution of bidiagonal systems with applications

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BIT 1999年第3期39卷 403-416页

作者： Bar-On, I Leoncini, M Technion Israel Inst Technol Dept Chem IL-32000 Haifa Israel Univ Pisa Dipartimento Informat IT-56125 Pisa Italy

We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.

关键词： linear systems triangular tridiagonal bidiagonal stable algorithms sensitivity analysis

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Divide and conquer algorithms for computing the eigendecomposition of symmetric diagonal-plus-semiseparable matrices

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NUMERICAL algorithms 2005年第4期39卷 379-398页

作者： Mastronardi, N Van Camp, E Van Barel, M CNR Ist Applicaz Calcolo Sez Bari I-70126 Bari Italy Katholieke Univ Leuven Dept Comp Sci B-3001 Louvain Belgium

Three fast and stable divide and conquer algorithms to compute the eigendecomposition of symmetric diagonal-plus-semiseparable matrices are considered.

关键词： semiseparable matrix fast algorithms stable algorithms eigendecomposition

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ON ACCURATE COMPUTATIONS OF THE PERRON ROOT

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1993年第2期14卷 456-467页

作者： ELSNER, L KOLTRACHT, I NEUMANN, M XIAO, D UNIV CONNECTICUT DEPT MATHSTORRSCT 06269

This paper establishes a new componentwise perturbation result for the Perron root of a non-negative and irreducible matrix. The error bound is independent of the angle between left and right Perron eigenvectors. It is shown that a known inverse iteration algorithm with new stopping criteria will have a small componentwise backward error, which is consistent with the perturbation result. Numerical experiments demonstrate that the accuracy of the Perron root computed by the proposed algorithm is, indeed, independent of the angle.

关键词： NONNEGATIVE MATRICES PERRON ROOT SPARSE SYSTEMS BACKWARD ERROR COMPONENTWISE PERTURBATIONS stable algorithms

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Row Compression and Nested Product Decomposition of a Hierarchical Representation of a Quasiseparable Matrix

Row Compression and Nested Product Decomposition of a Hierar...

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作者： Mary Hudachek-Buswell Georgia State University

学位级别：博士

This research introduces a row compression and nested product decomposition of an nxn hierarchical representation of a rank structured matrix A, which extends the compression and nested product decomposition of a quasiseparable matrix. The hierarchical parameter extraction algorithm of a quasiseparable matrix is efficient, requiring only O(nlog(n))operations, and is proven backward stable. The row compression is comprised of a sequence of small Householder transformations that are formed from the low-rank, lower triangular, off-diagonal blocks of the hierarchical representation. The row compression forms a factorization of matrix A, where A = QC, Q is the product of the Householder transformations, and C preserves the low-rank structure in both the lower and upper triangular parts of matrix A. The nested product decomposition is accomplished by applying a sequence of orthogonal transformations to the low-rank, upper triangular, off-diagonal blocks of the compressed matrix C. Both the compression and decomposition algorithms are stable, and require O(nlog(n)) operations. At this point, the matrix-vector product and solver algorithms are the only ones fully proven to be backward stable for quasiseparable matrices. By combining the fast matrix-vector product and system solver, linear systems involving the hierarchical representation to nested product decomposition are directly solved with linear complexity and unconditional stability. Applications in image deblurring and compression, that capitalize on the concepts from the row compression and nested product decomposition algorithms, will be shown.

关键词： Hierarchical matrices Row compression Nested product decomposition stable algorithms Quasiseparable matrices Image processing

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One-step finite-difference time-domain algorithm to solve the Maxwell equations

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Physical Review E 2003年第5期67卷 056706-056706页

作者： H. De Raedt K. Michielsen J. S. Kole M. T. Figge []Applied Physics–Computational Physics Materials Science Centre University of Groningen Nijenborgh 4 NL-9747 AG Groningen The Netherlands

We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from the Yee algorithm and from unconditionally stable algorithms. We demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite-difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.

关键词： .Time-Domain Solve Maxwell equations Unconditionally time step Finite-Difference stable algorithms one-step algorithm Yee algorithm

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