Browsing by Author "Matt, Urs von"
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Item Kassandra: The Automatic Grading System(1998-10-15) Matt, Urs vonAn automatic grading system is presented for grading assignments in scientific computing. A student can interactively use this system to check the correctness of his program assignments. The grade for a correct solution is automatically recorded. This paper also considers the security problems with such an automatic grading system. (Also cross-referenced as UMIACS-TR-94-59)Item The Orthogonal QD-Algorithm(1998-10-15) Matt, Urs vonThe orthogonal qd-algorithm is presented to compute the singular value decomposition of a bidiagonal matrix. This algorithm represents a modification of Rutishauser's qd-algorithm, and it is capable of determining all the singular values to high relative precision. A generalization of the Givens transformation is also introduced, which has applications besides the orthogonal qd-algorithm. The shift strategy of the orthogonal qd-algorithm is based on Laguerre's method, which is used to compute a lower bound for the smallest singular value of the bidiagonal matrix. Special attention is devoted to the numerically stable evaluation of this shift. (Also cross-referenced as UMIACS-TR-94-9.1)Item Rounding Errors in Solving Block Hessenberg Systems(1998-10-15) Matt, Urs von; Stewart, G. W.A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a backward stable solution. The algorithm is shown to be stable for diagonally dominant matrices and for M-matrices. (Also cross-referenced as UMIACS-TR-94-105)