FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308015496> ?p ?o ?g. }

• W4308015496 endingPage "1029" @default.
• W4308015496 startingPage "1029" @default.
• W4308015496 abstract "This issue of SIAM Review contains two papers in the Education section. The first, “A Generalized Dual Transform: Linear Algebra and Geometry of (Pseudo)Inverting a Matrix,” is presented by L. P. Withers, Jr. For a linear subspace $A$ of a vector space $V$, we may have a nonorthogonal basis of $A$. We could obtain an orthogonal basis (e.g., by the Gram--Schmidt orthogonalization procedure) and the orthogonality helps us to represent each element $bin A$ as a linear combination of the new basis in an easy way. How should we express $b$ as a linear combination of the original, unorthogonalized vectors? One suggestion is to construct a complementary list of vectors, called a dual list, such that each pair of vectors $a^i,a^j$ on that list are orthogonal and each vector has a length of one. The construction is called the dual transform. Involving the complementary subspace of $A$ in $V$ and orthogonal projections, we obtain again a simple formula for the representation of $b$. Next to generating dual vectors, the Gram--Schmidt orthogonalization procedure exhibits other interesting properties, which lead to a parallel so-called butterfly process for computing the dual transform. The article proceeds to explain how the dual transform is generalized via axioms and how the respective procedures are performed in the general setting. Several examples supplement the discussion. The paper is accessible to advanced undergraduate students with basic knowledge in linear algebra and complex analysis. The second article, “When Randomness Helps in Undersampling,” was written by Roel Snieder and Michael B. Wakin. In our digital era, we use many recordings: music, sounds of nature, and others. Many other signals such as telecommunication, temperature, and air pressure, are recorded for practical and scientific purposes. When signals are stored in computers, they are digitized by collecting and storing values of some functions at discrete times. A straightforward thought on how to accomplish that is to collect values uniformly in time and in all frequency components. However, the measurements might be feasible only for some times or frequencies; otherwise data acquisition or data transmission of a full collection might be too burdensome. When some times or frequencies are left out, it is said that the signal is undersampled. In that case, it is best to choose the times or frequencies to be left out randomly instead of uniformly. The authors focus on the problem of reconstructing a signal in the time domain using undersampled frequency components. The benefits of random undersampling are illustrated with an example of the air pressure recorded at a volcano in Costa Rica, but the authors cite other sources on seismic surveys as well as magnetic resonance imaging where benefits from undersampling are evidenced. The key to understand the phenomena is to analyze the effect of the sampling on the discrete Fourier transform, which allows a discrete-time signal of length $N$ to be represented as a sum of $N$ complex exponential terms. The authors have made the signal processing codes and the data that are used for the article available at https://mines.edu/~mwakin/software. The paper is directed toward undergraduate students in engineering with a mathematical background and interests." @default.
• W4308015496 created "2022-11-07" @default.
• W4308015496 creator A5044483915 @default.
• W4308015496 date "2022-11-01" @default.
• W4308015496 modified "2023-09-26" @default.
• W4308015496 title "Education" @default.
• W4308015496 doi "https://doi.org/10.1137/22n975585" @default.
• W4308015496 hasPublicationYear "2022" @default.
• W4308015496 type Work @default.
• W4308015496 citedByCount "0" @default.
• W4308015496 crossrefType "journal-article" @default.
• W4308015496 hasAuthorship W4308015496A5044483915 @default.
• W4308015496 hasConcept C11413529 @default.
• W4308015496 hasConcept C118615104 @default.
• W4308015496 hasConcept C121332964 @default.
• W4308015496 hasConcept C12362212 @default.
• W4308015496 hasConcept C12426560 @default.
• W4308015496 hasConcept C13336665 @default.
• W4308015496 hasConcept C136119220 @default.
• W4308015496 hasConcept C139352143 @default.
• W4308015496 hasConcept C17137986 @default.
• W4308015496 hasConcept C187064257 @default.
• W4308015496 hasConcept C202444582 @default.
• W4308015496 hasConcept C2524010 @default.
• W4308015496 hasConcept C33923547 @default.
• W4308015496 hasConcept C47559304 @default.
• W4308015496 hasConcept C62520636 @default.
• W4308015496 hasConceptScore W4308015496C11413529 @default.
• W4308015496 hasConceptScore W4308015496C118615104 @default.
• W4308015496 hasConceptScore W4308015496C121332964 @default.
• W4308015496 hasConceptScore W4308015496C12362212 @default.
• W4308015496 hasConceptScore W4308015496C12426560 @default.
• W4308015496 hasConceptScore W4308015496C13336665 @default.
• W4308015496 hasConceptScore W4308015496C136119220 @default.
• W4308015496 hasConceptScore W4308015496C139352143 @default.
• W4308015496 hasConceptScore W4308015496C17137986 @default.
• W4308015496 hasConceptScore W4308015496C187064257 @default.
• W4308015496 hasConceptScore W4308015496C202444582 @default.
• W4308015496 hasConceptScore W4308015496C2524010 @default.
• W4308015496 hasConceptScore W4308015496C33923547 @default.
• W4308015496 hasConceptScore W4308015496C47559304 @default.
• W4308015496 hasConceptScore W4308015496C62520636 @default.
• W4308015496 hasIssue "4" @default.
• W4308015496 hasLocation W43080154961 @default.
• W4308015496 hasOpenAccess W4308015496 @default.
• W4308015496 hasPrimaryLocation W43080154961 @default.
• W4308015496 hasRelatedWork W1494474111 @default.
• W4308015496 hasRelatedWork W1515059119 @default.
• W4308015496 hasRelatedWork W2081762384 @default.
• W4308015496 hasRelatedWork W2982406148 @default.
• W4308015496 hasRelatedWork W2990024850 @default.
• W4308015496 hasRelatedWork W4225395080 @default.
• W4308015496 hasRelatedWork W4232228426 @default.
• W4308015496 hasRelatedWork W4283322789 @default.
• W4308015496 hasRelatedWork W4308015496 @default.
• W4308015496 hasRelatedWork W583117815 @default.
• W4308015496 hasVolume "64" @default.
• W4308015496 isParatext "false" @default.
• W4308015496 isRetracted "false" @default.
• W4308015496 workType "article" @default.