### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Adv Sci Computing I CS 6210

The U

GPA 3.78

### View Full Document

## 23

## 0

## Popular in Course

## Popular in ComputerScienence

This 24 page Class Notes was uploaded by Marian Kertzmann DVM on Monday October 26, 2015. The Class Notes belongs to CS 6210 at University of Utah taught by Christopher Sikorski in Fall. Since its upload, it has received 23 views. For similar materials see /class/229979/cs-6210-university-of-utah in ComputerScienence at University of Utah.

## Popular in ComputerScienence

## Reviews for Adv Sci Computing I

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15

x39sx dgw e a Sud nd lxlzixnz 47 a x xa zxfanxg W amp 1quot T T llx39l 1 x 1quot 3x4ch 39xdu a i 2 a nu 437 4 an flu I amp o 39 so 2 x7 at Iv i J m and x 3 HM X It b new n it Ska n z I 2 ww39r vx CSSuImIna quotW 39 c 1 48 qs qupu hgs assume quotW z in 4 srfr awwnet ki T 1 E 2 f7f 39 e 4 134 J os39Hwoaonal 3uH51 LL 39 Vxe l8 Hx lzt quotxl 39rololem 6 X R Hquot tie 39 Squ aif 39 tin61 e1 3 10 Dire R e m a n J D 09an 49 quotHI 2WT as Uc hcz x1239g 391 139 ti iM 39 12 73 0 H I is I X 1lxl xz x a 0 Sire Ruici w a 1 45m w lel xli X3 i 50 g 1 hi x 4 signalir 4 IXI p 2 3149 m e1 i 5 mw A 75 53 54 duv PMquot If n z n mg 3x3 39 V 393 Z n 3 k I 2X K39f 39239 Eva a 2 g I k2 xll Ii 2x llx 4fo V 39 a 1 11111 1 x lfx39 a 339 k22 XII his x u a 1 2 m may 3 x 55 mm m W 6qu WW n 39 39quot 97E 9 0 i a a 4 3 g H Iwa A H10 Iwa c 4 a Mfuraf f m half 56 58 due on dis Fibs 31K s6 1 vzilxhe 25 r w b x 2 quotb KA H 53 M 1 WW5 H 4 39 was 5 a MM HEMquot MEWS H PM My quotWK 2 itquot quot W v quot I r M 4 Judo9 quota 3 N mm man2quot NM wV M39WxM u 01 442 ii Mp ovalw 1 f 5 32 4 39 Juice as expensive as Gaussian EL MEMa ou um 2 464 v 59 50 v 455 4 mm 39 5quotquot quot a m d ram 4 Q 9 2 V x gt0 39 2 PH 4 Fm i JYOua Iad vc Scat t39bn of aching radius nal Pm I 117 V e P Pumdukon mamx f PH P 13 60 c quot quot vcd of 3 dovdk quotaf x 6 Sine we 3a mt X r s 33gc x Bx c x quot 39 3Rg quotKN 1 3quot B x x HBI Max 62 59 FM 3 X 5 X comavac 9 a 3 Max i i A 939 Gianvalue 4 3 Nowww V8 0 3 5 e M v a gt Mu s stewequot Mun smaller 35 Ju I I 6 3 b V Iquot X J D p S 6 R M nr 3 06 J 4 395 J U x 4 L J 6am 3 Set 1 J I 5 If 41150 3 5 tag 1 O sca den 65 50R successive ww dunked In 6aan Sadat ne39 but 66 33 D xi 3 I 9 Dxi 399 w Na UK 6 yuL iH UD U Xe 605 QM r v X130 3 DHnU 03963 U I UCD QU b p minimizing 38 g lemma V OJ 3 5 M wcc c we a 2 67 68 3 K PFO C355 A 9 1 2 mquot39391 g 1 E lt 12 mquotquot1 242 and although the computed value will depend on the order in which the multiplications and divisions are performed the bounds are again indepen dent of that order The computed value g has a low relative error for any reasonable values of m and n 25 For extended sequences of additions it is no longer true that the computed value necessarily has a low relative error even though this was true for the sum of two numbers with the more accurate round o 39 rule In fact there is no useful bound for 1 flx1x2 xnx1x2 xnf 251 i3 39 j since the oatingpoint sum may be Zero when the true sum is not and versa Note that we use flx1xz x to denote the computed sum when additions take place in the order in which they are written quot f It is still true however that 9n flx1x2 xn as x x x if vvhere each x differs from x by a factor which is close to unity We de ne the quantities s recursively by the relations 91 x1 252 s Efl8r1xr s1x1egt 253 I 16 lt 2 4 254 Combining these equations we have quot sn 5 x1l 171 x21 772 xnl 77 255 12 162l6316n 256 1 77 1e1e391 1en r 2 n 257 12 quot 1 ltt l 771 lt 1 2 quotquot1 258 1 2n1r lt 1 7 s 12 n1 r r 2 n 259 Note that x1 and 62 have the same factor which is not surprising since they quot1play identical roles It is inconvenient that the factor associated with x1 is 53 jg39 not de ned by the same formula as the others and it is often simpler to write 1 2tn1r s 1 17 lt 12 n1r r 1 n 2510 which is true a fortiorz39 Note that the bounds themselves are dependent on the order of summation The upper bound for the error is smallest if the terms are added in order of s39increasing absolute magnitude since then the largest factor 1171 is quot filquotquotquotlassociated with the smallest xi Although this gives the smallest upper 39gbound it does not necessarily give the smallest error in practice Consider gffOr example the sum 1040 1025 1030 9123 102 0399663 39100399315 If we add them in the natural order we haVe 17 5210301127 3310201607 s4391006755 and there are no rounding errors at any stage If we add the numbers in the opposite order then we have 32 wit 01059 33 104 01018 s4 1007000 and there are rounding errors at each of the rst two stages It will be appreciated that this example is rather special The more normal case is illustrated by the following example Consider the sum 10804462 10 306412 10302413 1000 1234 If the additions take place in the order in which the terms are given the computed sum is 1000 39 1247 and the errors made in the three additions are 10 04 10 6 03 and 10 4 028 If they are added in the reverse order the computed sum is 100039124396 and the errors in the three additiOns ii are 104 0413 104 0412 and 104 0462 Adding the terms of smallest modulus rst ensures that the rounding errors made in the early stages are small Clearly if we include a large number of terms of order 10quot3 in a sum of the above type then the advantage of adding the small I terms rst can be very considerable a 26 We now consider the error made when an innerproduct is Computed in oatingpoint We write 5 f1a161a262 anbn 261 The notation implies that a and 6 are standard oating point numbers The products are computed rst and then added in the order in which they are written We de ne the quantities 3 and t recursively by the relations t flab 262 31 t1 3 fls139 t 263 From these relations we deduce tr 5 arbr1 r IErl lt 2quot 264 s a s1tgt1n lan lt 24 265 and hence Sn a161161 02621 62 anbn1 6 266 1 61 1El1 172 1nn 267 16 161n 141 r2 n 268 Hence I 1 24quot ltlt 161 lt 12tn 269 t6lt12t r2 r2n 2610 18 1 z tn r2 g 1

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I made $350 in just two days after posting my first study guide."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.