氏名 豊永 憲治
研究業績等に関する事項(※原則として直近５年間の業績を表示）
著書，学術論文等の名称 単著，
共著の別		 発行又は
発表の年月		 発行所，発表雑誌等
又は発表学会等の名称
学術論文
１．Computation of values of threshold probabilities of discounted Markov decision processes with guaranteed accuracy 単著 2000 Surikaisekikenkyusho Kokyuroku, No. 1147, (2000.4), 78-87
２．Numerical Enclosure for the Optimal Threshold Probability in Discounted Markov Decision Processes 共著 2000 Bulletin of Informatics and Cybernetics,32, (2000.6),81-90
３．Optimal Policy for Minimizing Risk Models in Markov Decision Processes 共著 2002 Journal of Mathematical Analysis and Applications,271,(2002.7),66-81
４．Verified numerical computations for multiple or nearly multiple eigenvalue operators 共著 2002 Journal of Computational and Applied Mathematics,147,(2002.10),
175-190
５．An improvement of the enclosure method for elliptic eigenvalue problems 共著 2002 Proceedings of Fifth China-Japan Seminar on Numerical Mathematics
６．Equivalence classes for optimizing risk models in Markov decision processes
 共著 2004 Mathematical Methods of Operations Research,60,(2004.10),239-250
７．A method for separating nearly multiple eigenvalues for an Hermitian matrix 単著 2007 Journal of Computational and Applied Mathematics,199(2),(2007.2),
432-436
８．Numerical enclosure for multiple eigenvalues of an Hermitian matrix
whose graph is a tree
 共著 2009 Linear Algebra and Its Applications, 431, (2009.11),1989-1999
９．Application of an identity for subtrees with a given eigenvalue 共著 2015 Electronic Journal ofLinear Algebra,30, (2015.12), 964-973
１０．The classification
of edges and the change in multiplicity of an
eigenvalue of a real symmetric matrix resulting from the change in
an edge value
 共著 2017 Special Matrices, 5 (2017.1), 51-60
１１．Multiplicities : Adding a Vertex to a Graph 共著 2017 Springer Proceedings in Mathematics & Statistics, 192 (2017.3), 117-126
１２．Classification of vertices and edges with respect to the geometric multiplicity of an eigenvalue in a matrix, with a given graph, over a field 共著 2018 Linear and Multilinear Algebra, 66(11), (2018), 2168-2182
１３．The Change in Multiplicity of an Eigenvalue of a Real Symmetric Matrix Resulting from
the Changes in Edge Values Around a Classified Vertex in a Tree
 単著 2018 Acta Mathematica Vietnamica, 43 (2018.6), 641-647
１４．The change in multiplicity of an eigenvalue due to adding or removing edges 共著 2019 Linear algebra and its applications, 560 (2019.1), 86-99
１５．The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree
 単著 2019 Special Matrices, 9,(2019.12),257-262
１６．数学の遠隔授業の実践と学生の状況について 単著 2021 日本数学教育学会 高専・大学部会論文誌 (27)
１７．The Effect of Perturbation of an Off-diagonal Entry Pair on the Geometric Multiplicity of an Eigenvalue 共著 2021 Linear algebra and its applications 615 112-142
１８．Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue 共著 2021 Linear and Multilinear Algebra 69(10) 1803-1812
１９．Change in vertex status after removal of another vertex in the general setting 共著 2021 Linear algebra and its applications 612 128-145
２０．The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue 単著 2023 Special Matrices 11,
２１．Parter Vertices and Generalization of the Downer Branch Mechanism in the General Setting 共著 2024 Linear and Multilinear Algebra 72(8) 1239-1253