Rank revealing Gaussian elimination by the maximum volume concept

Amaranth flour from germinated (GA) and non-germinated (A) seeds (0%-C, 5%, 15%, 25%) were mixed with wheat flour for breadmaking. Fermentation parameters of dough (time-tf, maximum volume-Vmax) were obtained. Specific volume (Vsp) of breads, crust color, texture and relaxation of crumb were analyzed. A high amount of germinated amaranth flour decreased Vmax and increased tf, obtaining breads with low Vsp and darkness crust. A firmed and chewy crumb, although with a more aerated structure (high area occupied by alveoli) was obtained. The GA25 bread presented the softer crumb. The elastic modulus-E1 of crumb increased and the relaxation time-T1 decreased with higher amounts of amaranth flour, suggesting the formation of a more structured crumb; mainly in the case of non-germinated amaranth flour. Wheat flour resisted the inclusion of 25% of germinated amaranth seeds (GA25) without substantial changes in bread quality.

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Replacing Pivoting in Distributed Gaussian Elimination with Randomized Techniques

2020 IEEE/ACM 11th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA) ◽

10.1109/scala51936.2020.00010 ◽

2020 ◽

Author(s):

Neil Lindquist ◽

Piotr Luszczek ◽

Jack Dongarra

Keyword(s):

Gaussian Elimination

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Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

BIT Numerical Mathematics ◽

10.1007/s10543-021-00872-1 ◽

2021 ◽

Author(s):

Stefano Massei

Keyword(s):

Computer Science ◽

Recent Work ◽

Linear Algebra ◽

Optimization Problems ◽

Approximation Error ◽

Positive Semidefinite ◽

Numerical Linear Algebra ◽

Maximum Volume ◽

Deterministic Algorithms ◽

Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

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An Implementation of Gaussian Elimination with Partial Pivoting for Sparse Systems

SIAM Journal on Scientific and Statistical Computing ◽

10.1137/0906028 ◽

1985 ◽

Vol 6 (2) ◽

pp. 390-409 ◽

Cited By ~ 38

Author(s):

Alan George ◽

Esmond Ng

Keyword(s):

Gaussian Elimination ◽

Partial Pivoting ◽

Sparse Systems

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Autogenous bone augmentation from the zygomatic alveolar crest: a volumetric retrospective analysis in the maxilla

International Journal of Implant Dentistry ◽

10.1186/s40729-020-00258-y ◽

2020 ◽

Vol 6 (1) ◽

Author(s):

Irina Kuster ◽

Livia Osterwalder ◽

Silvio Valdec ◽

Bernd Stadlinger ◽

Maximilian E. H. Wagner ◽

...

Keyword(s):

Gold Standard ◽

Donor Site ◽

Bone Defects ◽

Donor Site Morbidity ◽

Bone Volume ◽

Autogenous Bone ◽

Bone Augmentation ◽

Maximum Volume ◽

Alveolar Crest ◽

Good Access

Abstract Background Autogenous bone augmentation is the gold standard for the treatment of extended bone defects prior to implantation. Bone augmentation from the zygomatic crest is a valuable option with several advantages, but the current literature for this treatment is scant. The aim of this study was to evaluate the increase in bone volume after locoregional bone augmentation using autogenous bone from the zygomatic alveolar crest as well as the complications and success rate. Results Analysis of the augmented bone volume in seven patients showed a maximum volume gain of 0.97 cm3. An average of 0.54 cm3 of autogenous bone (SD 0.24 cm3; median: 0.54 cm3) was augmented. Implantation following bone augmentation was possible in all cases. Complications occurred in three patients. Conclusion The zygomatic alveolar crest is a valuable donor site for autogenous alveolar onlay grafting in a locoregional area such as the maxillary front. Low donor site morbidity, good access, and its suitable convexity make it a beneficial choice for autogenous bone augmentation.

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