"Lanczos Tridiagonalization and Core Problems" . "linear approximation problem; orthogonal transformation; core problem; Golub-Kahan bidiagonalization; Lanczos tridiagonalization; Jacobi matrix"@en . "Strako\u0161, Zden\u011Bk" . "RIV/67985807:_____/07:00032522!RIV07-AV0-67985807" . "Lanczo\u0161ova t\u0159\u00EDdiagonalizace a core probl\u00E9my"@cs . . . . "[DA1488764EB9]" . "Lanczos Tridiagonalization and Core Problems"@en . "Lanczo\u0161ova t\u0159\u00EDdiagonalizace a core probl\u00E9my"@cs . "0024-3795" . "2-3" . . . "The paper %22C.C. Paige, Z. Strako\u0161: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)%22 presents a core problem formulation of orthogonally invariant linear approximation problems Ax ~ b, that extracts the necessary and sufficient information for solving the origin\u00E1l problem. Our contribution derives the fundamental characteristics of the core problem from the known relationship between the Golub-Kahan bidiagonalization and the Lanczos tridiagonalization."@en . . "Hn\u011Btynkov\u00E1, Iveta" . . . "RIV/67985807:_____/07:00032522" . "The paper %22C.C. Paige, Z. Strako\u0161: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)%22 presents a core problem formulation of orthogonally invariant linear approximation problems Ax ~ b, that extracts the necessary and sufficient information for solving the origin\u00E1l problem. Our contribution derives the fundamental characteristics of the core problem from the known relationship between the Golub-Kahan bidiagonalization and the Lanczos tridiagonalization." . . . "243;251" . . . "430474" . "Lanczos Tridiagonalization and Core Problems" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "Lanczos Tridiagonalization and Core Problems"@en . "2"^^ . "V \u010Dl\u00E1nku %22C.C. Paige, Z. Strako\u0161: Core problems in linear algebraic systems (SIAM J. Matrix Anal. Appl. 27 (2006), pp. 861-875)%22 je definov\u00E1n a pops\u00E1n pojem core probl\u00E9mu v ortogon\u00E1ln\u011B invariantn\u00EDch aproxima\u010Dn\u00EDch \u00FAloh\u00E1ch Ax ~ b, kter\u00FD extrahuje nutn\u00E9 a posta\u010Duj\u00EDc\u00ED informace pro \u0159e\u0161en\u00ED uveden\u00E9 \u00FAlohy. V tomto \u010Dl\u00E1nku odvod\u00EDme z\u00E1kladn\u00ED vlastnosti core probl\u00E9mu ze zn\u00E1m\u00FDch vztah\u016F mezi Lanczo\u0161ovou t\u0159\u00EDdiagonalizac\u00ED a Golub-Kahanovou bidiagonalizac\u00ED."@cs . "Linear Algebra and Its Applications" . "P(1ET400300415), Z(AV0Z10300504)" . "9"^^ . . "2"^^ . "421" . . . . . .