SIAM ReviewPub Date : 2022-08-01DOI: 10.1137/20m1387948
A. Wathen
{"title":"Some Comments on Preconditioning for Normal Equations and Least Squares","authors":"A. Wathen","doi":"10.1137/20m1387948","DOIUrl":"https://doi.org/10.1137/20m1387948","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"21 1","pages":"640-649"},"PeriodicalIF":10.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77377388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-08-01DOI: 10.1137/20m1321140
Qinmeng Zou, F. Magoulès
{"title":"Delayed Gradient Methods for Symmetric and Positive Definite Linear Systems","authors":"Qinmeng Zou, F. Magoulès","doi":"10.1137/20m1321140","DOIUrl":"https://doi.org/10.1137/20m1321140","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"78 1","pages":"517-553"},"PeriodicalIF":10.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80829303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-08-01DOI: 10.1137/21m1391481
M. Gaudioso, J. Hiriart-Urruty
{"title":"Deforming $||.||_{1}$ into $||.||_{infty}$ via Polyhedral Norms: A Pedestrian Approach","authors":"M. Gaudioso, J. Hiriart-Urruty","doi":"10.1137/21m1391481","DOIUrl":"https://doi.org/10.1137/21m1391481","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"4 1","pages":"713-727"},"PeriodicalIF":10.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73701075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-08-01DOI: 10.1137/21m1402868
Demi L. Gandy, M. R. Nelson
{"title":"Analyzing Pattern Formation in the Gray-Scott Model: An XPPAUT Tutorial","authors":"Demi L. Gandy, M. R. Nelson","doi":"10.1137/21m1402868","DOIUrl":"https://doi.org/10.1137/21m1402868","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"90 1","pages":"728-747"},"PeriodicalIF":10.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85204860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-07-07DOI: 10.1137/22M1505840
P. Guasoni, Yu‐Jui Huang
{"title":"Minimizing the Repayment Cost of Federal Student Loans","authors":"P. Guasoni, Yu‐Jui Huang","doi":"10.1137/22M1505840","DOIUrl":"https://doi.org/10.1137/22M1505840","url":null,"abstract":". Federal student loans are fixed-rate debt contracts with three main special features: (i) borrowers can use income-driven schemes to make payments proportional to their income above subsistence, (ii) after several years of good standing, the remaining balance is forgiven but taxed as ordinary income, and (iii) accrued interest is simple, i.e., not capitalized. For a very small loan, the cost-minimizing repayment strategy dictates maximum payments until full repayment, forgoing both income-driven schemes and forgiveness. For a very large loan, the minimal payments allowed by income-driven schemes are optimal. For intermediate balances, the optimal repayment strategy may entail an initial period of minimum payments to exploit the non-capitalization of accrued interest, but when the principal is being reimbursed maximal payments always precede minimum payments. Income-driven schemes and simple accrued interest mostly benefit borrowers with very large balances. MSC (2010): 91G20, 91G80.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"105 1","pages":"689-709"},"PeriodicalIF":10.2,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79540102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-05-01DOI: 10.1137/21m1395922
Bernardo Gouveia, H. Stone
{"title":"Generating Resonant and Repeated Root Solutions to Ordinary Differential Equations Using Perturbation Methods","authors":"Bernardo Gouveia, H. Stone","doi":"10.1137/21m1395922","DOIUrl":"https://doi.org/10.1137/21m1395922","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"29 5","pages":"485-499"},"PeriodicalIF":10.2,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72475552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-05-01DOI: 10.1137/22m1476915
Frantisek Kardos
{"title":"Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes","authors":"Frantisek Kardos","doi":"10.1137/22m1476915","DOIUrl":"https://doi.org/10.1137/22m1476915","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"3 1","pages":"425-465"},"PeriodicalIF":10.2,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78429685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-02-01DOI: 10.1137/21m1446769
G. Linderman, S. Steinerberger
{"title":"Dimensionality Reduction via Dynamical Systems: The Case of t-SNE","authors":"G. Linderman, S. Steinerberger","doi":"10.1137/21m1446769","DOIUrl":"https://doi.org/10.1137/21m1446769","url":null,"abstract":"","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"12 1","pages":"153-178"},"PeriodicalIF":10.2,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88818900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM ReviewPub Date : 2022-02-01DOI: 10.1137/20m1358694
G. Strang, C. Moler
{"title":"LU and CR Elimination","authors":"G. Strang, C. Moler","doi":"10.1137/20m1358694","DOIUrl":"https://doi.org/10.1137/20m1358694","url":null,"abstract":"Abstract The reduced row echelon form rref (A) has traditionally been used for classroom examples : small matrices A with integer entries and low rank r. This paper creates a column-row rank-revealing factorization A = CR, with the first r independent columns of A in C and the r nonzero rows of rref (A) in R. We want to reimagine the start of a linear algebra course, by helping students to see the independent columns of A and the rank and the column space. If B contains the first r independent rows of A, then those rows of A = CR produce B = W R. The r by r matrix W has full rank r, where B meets C. Then the triple factorization A = CW B treats columns and rows of A (C and B) in the same way.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"49 1","pages":"181-190"},"PeriodicalIF":10.2,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90230426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}