Special issue on state of the art in self-validating numerical computations
VOL. 26 · NO. 2-3 | October 2009
 
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Articles
Masaaki Sugihara
Japan J. Indust. Appl. Math. 26 (2-3), 123, (October 2009)
KEYWORDS: 65-06
No abstract available
Mitsuhiro T. Nakao, Shin'ichi Oishi
Japan J. Indust. Appl. Math. 26 (2-3), 123-124, (October 2009)
No abstract available
Teruo Sunaga
Japan J. Indust. Appl. Math. 26 (2-3), 125-143, (October 2009)
KEYWORDS: 65G30
Kohshi Okumura
Japan J. Indust. Appl. Math. 26 (2-3), 145-167, (October 2009)
KEYWORDS: interval operation, Krawczyk--Moore--Jones's algorithm, parallel algorithm, FPGA implementation, Gray code, all solutions
Takeshi Ogita, Shin'ichi Oishi
Japan J. Indust. Appl. Math. 26 (2-3), 169-190, (October 2009)
KEYWORDS: verified numerical computation, verified solutions of linear systems, self-validating methods
Stef Graillat, Philippe Langlois, Nicolas Louvet
Japan J. Indust. Appl. Math. 26 (2-3), 191-214, (October 2009)
KEYWORDS: polynomial evaluation, compensated algorithm, floating-point arithmetic, IEEE-754
Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Japan J. Indust. Appl. Math. 26 (2-3), 215-231, (October 2009)
KEYWORDS: robust geometric predicate, 2D orientation problem, floating-point arithmetic, accurate algorithm
Yoshitaka Watanabe
Japan J. Indust. Appl. Math. 26 (2-3), 233-247, (October 2009)
KEYWORDS: numerical verification, two-coupled equations, fixed-point theorem
Siegfried M. Rump
Japan J. Indust. Appl. Math. 26 (2-3), 249-277, (October 2009)
KEYWORDS: extremely ill-conditioned matrix, condition number, multiplicative correction, accurate dot product, accurate summation, error-free transformations
Günter Mayer
Japan J. Indust. Appl. Math. 26 (2-3), 279-296, (October 2009)
KEYWORDS: interval linear system, solution set, interval hull, interval Gaussian algorithm, interval Cholesky method, interval Trench algorithm, interval Bareiss algorithm
Goetz Alefeld
Japan J. Indust. Appl. Math. 26 (2-3), 297-315, (October 2009)
KEYWORDS: fixed point iteration, Newton-like methods, nonsmooth equation
Xiaojun Chen
Japan J. Indust. Appl. Math. 26 (2-3), 317-325, (October 2009)
KEYWORDS: verification, spherical designs, system of nonlinear equations
Yusuke Nakaya, Tetsuo Nishi, Shin'ichi Oishi, Martin Claus
Japan J. Indust. Appl. Math. 26 (2-3), 327-336, (October 2009)
KEYWORDS: nonlinear equations, Existence of solution, Krawczyk's method, transistor circuit
Christian Jansson
Japan J. Indust. Appl. Math. 26 (2-3), 337-363, (October 2009)
KEYWORDS: linear programming, semidefinite programming, conic programming, Convex programming, Combinatorial optimization, rounding errors, Ill-posed problems, interval arithmetic, branch-bound-and-cut
Nobito Yamamoto, Takashi Komori
Japan J. Indust. Appl. Math. 26 (2-3), 365-392, (October 2009)
KEYWORDS: Taylor model, Nakao method, validated computation, ODEs
Zin Arai, Hiroshi Kokubu, Paweł Pilarczyk
Japan J. Indust. Appl. Math. 26 (2-3), 393-417, (October 2009)
KEYWORDS: dynamical system, rigorous computations, algorithm, Conley index, hyperbolic dynamics
Michael Plum
Japan J. Indust. Appl. Math. 26 (2-3), 419-442, (October 2009)
KEYWORDS: elliptic boundary value problem, semilinear, computer-assisted proof, existence, enclosures, error bounds, multiplicity
Yoshitaka Watanabe, Mitsuhiro T. Nakao
Japan J. Indust. Appl. Math. 26 (2-3), 443-463, (October 2009)
KEYWORDS: numerical verification method, elliptic equations, Rayleigh--Bénard problem, bifurcation point
Shin'ichi Oishi, Takeshi Ogita, Siegfried M. Rump
Japan J. Indust. Appl. Math. 26 (2-3), 465-476, (October 2009)
KEYWORDS: iterative refinement, verified numerical computation, ill-conditioned linear systems
Kaori Nagatou
Japan J. Indust. Appl. Math. 26 (2-3), 477-491, (October 2009)
KEYWORDS: numerical verification method, infinite dimensional eigenvalue problem, error estimates
Kenta Kobayashi
Japan J. Indust. Appl. Math. 26 (2-3), 493-516, (October 2009)
KEYWORDS: finite element method, a priori error estimation, Poisson equation
Masaaki Kanno, Hirokazu Anai
Japan J. Indust. Appl. Math. 26 (2-3), 517-530, (October 2009)
KEYWORDS: algebraic methods, control systems design, guaranteed accuracy computation, validated numerical methods, interval methods
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