PPT-Use the Linear Approximation to estimate

How accurate is your estimate Differential Notation The Linear Approximation to y f x is often written using the differentials dx and dy In this notation dx is used instead of . Numerical Solutions of Equations. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 2. nd. January 2014. y. = x. y = . cos. (x). Iterative Methods. Suppose we wanted to find solutions to . Matt Weinberg. MIT .  Princeton  MSR. References: . . http. ://arxiv.org/abs/. 1305.4002. http. ://arxiv.org/abs/. 1405.5940. http. ://arxiv.org/abs/. 1305.4000. Recap. Costis. ’ Talk: . Optimal multi-dimensional mechanism: additive bidders, no constraints. Differentials and Linear Approximation. BC Calculus. Related Rates :. How . fast . is . y . changing as . x . is changing?. -. Differentials:. How . much. does . y . change as . x . changes?. M. Matsui.. Linear Cryptanalysis Method for DES Cipher. . EUROCRYPT 93, 1994. . The first experimental cryptanalysis of the Data Encryption Standard. . CRYPT0 94, 1994. . Linear Approximations. A function with one bit output is a linear function over if output is XOR of input bits.. Session 4. Contents. Linear cryptanalysis. Differential cryptanalysis. 2. /48. Linear cryptanalysis. Known plaintext attack. The cryptanalyst has a set of plaintexts and the corresponding ciphertexts. Alexandr. . Andoni. . (Simons Institute). Robert . Krauthgamer. . (. Weizmann. . Institute). Ilya Razenshteyn . (CSAIL MIT). 1. Sketching. Compress a massive object to a . small. . sketch. Rich theories: . Actual area under curve:. Left-hand rectangular approximation:. Approximate area:. (too low). Approximate area:. Right-hand rectangular approximation:. (too high). Averaging the two:. 1.25% error. (too high). . for Binary . Pairwise. Energies. Lena . Gorelick. . joint work with. . O. . Veksler. I. Ben . Ayed. A. Delong. . Y. . Boykov. Example of Simple Binary Energy. 2. Potts Model. Binary . Pairwise. in mechanism design. Shuchi Chawla. University of Wisconsin – Madison. FOCS 2012. So far today…. Revenue & Social Welfare. This talk:. Non-linear functions of type & allocation. Question: how well can we optimize in strategic settings?. Rayleigh-Ritz method approximate solution in the entire beam. Difficult to find good approximate solution (discontinuities in derivatives). Finite element approximates solution in an element. In a small element simple functions are acceptably accurate. Math 200. Week 6 - Friday. Math 200. Goals. Be able to compute the . local linear approximation. for a function of two or more variables at a given point.. Be able to use a local linear approximation to estimate a given quantity.. Local Linearity. If a function is differentiable at a point, it is at least locally linear.. Differentiable. Local Linearity. If a function is differentiable at a point, it is at least locally linear.. Remark: Re = , also a linear combination of the yi's, hence É 5) The sum of the coefficients in (4) is = = = 1. Sampling distrib (linear mean function) ¥ V (independence) The new assumptio Remark Re also a linear combination of the yis hence 5 The sum of the coefficients in 4 is 1 Sampling distrib linear mean function Vindependence The new assumption means we can consx1