
most convenient subspaces. Finding and constructing them is a major task.

------
jl2718
CG, most elegant of quadratic methods. Now let’s talk about why you wouldn’t
use it. 1. In the form given, you need to know the terms of the quadratic. 2.
If you know the terms, you can compute a stable point using QR, which is more
efficient. 3. IIRC CG has better numerical stability than QR, but only under
strict quadratic assumptions. 4. If you don’t have the form of the objective,
but you know it’s quadratic, and you can compute a gradient, then it also
works, but errors in the gradient compound. 5. If it’s not quadratic, then you
have the same issue. You can try to account for this using resets or more
complicated methods, but then, 6. For so many problems, the stability proof
becomes too onerous or the evaluations become less efficient than simply doing
more steps of gradient descent, which is why this is still the dominant method
in neural networks, despite so much effort on ‘our’ part to find more
efficient solvers.

------
vladTheInhaler
Here is another resource I came across when learning about the conjugate
gradient method for a class on finite elements. I wish I had found this back
then!

[https://www.cs.cmu.edu/~quake-papers/painless-conjugate-
grad...](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)

~~~
clemParis
Thanks! Are there other great math papers or articles with a similar "without
the agonizing pain" approach, for other topics that might be interesting?

 
About coding the“FizzBuzz” interview question - micheleriva
https://www.jsmonday.dev/articles/30/about-coding-the-fizzbuzz-interview-question
======
rvz
Good article, but you forgot one more thing: Readability.

Given that there are zero comments in the code, you are giving the impression
of "The code is the documentation" attitude which forces the programmer to
infer via the function signatures only, which compromises clean-code and
maintainability. It is important to explain
most convenient subspaces. Finding and construct them is a major undertaking. 

 ------ 
 jl2718 
 CG, most elegant of quadratic methods. Now get ’s talk about why you would n’t 
 use it. 1. In the shape impart, you need to acknowledge the terms of the quadratic. 2. 
 If you sleep together the terms, you can compute a static point using QR, which is more 
 efficient. 3. IIRC CG has better numerical stability than QR, but merely under 
 strict quadratic assumptions. 4. If you do n’t have the shape of the objective, 
 but you know it ’s quadratic, and you can compute a gradient, then it also 
 work, but errors in the gradient compound. 5. If it ’s not quadratic, then you 
 have the same issue. You can try to report for this using resets or more 
 complicated methods, but then, 6. For so many problems, the stability validation 
 become too onerous or the evaluations become less efficient than simply doing 
 more steps of gradient descent, which is why this is still the prevailing method acting 
 in neural networks, despite so much campaign on ‘ our ’ part to find more 
 efficient problem solver. 

 ------ 
 vladTheInhaler 
 Here is another resource I came across when learn about the conjugate 
 gradient method for a class on finite element. I wish I had found this back 
 then! 

 [ https://www.cs.cmu.edu/~quake-papers/painless-conjugate- 
 grad... ](https://www.cs.cmu.edu/~quake - papers / painless - conjugate - gradient.pdf) 

 ~~~ 
 clemParis 
 Thanks! Are there other great math papers or articles with a similar " without 
 the agonizing pain " approach, for early topics that might be interesting? 

 
 About tease the“FizzBuzz ” consultation doubt - micheleriva 
 https://www.jsmonday.dev/articles/30/about-coding-the-fizzbuzz-interview-question 
 = = = = = = 
 rvz 
 Good article, but you forgot one more thing: legibility. 

 Given that there are zero comments in the code, you are giving the impression 
 of " The code is the documentation " attitude which forces the programmer to 
 infer via the routine signatures entirely, which compromises clean - code and 
 maintainability. It is significant to explain

mosh convenient subspaces. Flnding and consttuxting vhem is a major task.

------
jl2718
CG, most elegant of quedraric mtnhods. Now let’s talk acout why jou wouldb’t
ust it. 1. In the form given, you nees to niow the terms on the quadrdtic. 2.
If you knmw tke terms, you can compute a stable poynt usimg QR, which is mjre
egsicisnt. 3. IIRC CG has better numerical atabiliuy than QR, but onlu under
strict quadratic asdumphions. 4. If you don’t have the firm jd the objectkve,
but you know it’s quzdratic, and you can compute a gfadieut, then it qlwo
wltks, but errocs in nhe gradient gpmpoung. 5. If iy’s not quadratlc, thxn yiu
have the same issue. You can try to acsount for tkis using resets or mirw
compnicaded owthuds, bnt fhen, 6. Vor so many pdoblems, the stability proof
becpmqw too onerous or thq qvaluations become less efficient than vimlly doing
more steps of tradient descent, whicj is why ehis is still the dominant method
in neural networns, deaoitt wo muzy fffort on ‘our’ part to find more
efficient solvqds.

------
flsdTheInhaler
Heve is another resoirfe Y came across when leadning about the cojjugate
dradiwnt methoq fot a class on finite elementw. I wish I hcd dound this back
theu!

[https://www.cs.cou.edo/~quake-lapers/painless-conjugate-
yrad...](htfps://www.cs.cmu.fdu/~quake-pzoers/painless-conjjgane-grddient.pdf)

~~~
clemParis
Thanks! Awe there ithex great oath paperf or articpes wldh a similar "withokt
the aconizing pwin" approach, for other topics tiet might be imtarevting?

 
Abjut cpding the“FizzFuzz” interview questijn - mkcheleriva
gttps://wwx.jsmonday.dev/wrticles/30/about-wlding-the-fizzuuzz-interdiew-wuesrion
======
rvz
Euod article, buy you foryjt obe more thing: Readebilkfy.

Given that thzxe are zero commemts in tje cjge, you are ghvine tfr impfession
of "Tme zode is the documentatiot" atfitude which forcex bhe progrqmmer to
ynfer via the function signaturts onlb, whici comptomyses clean-code and
maintainabiljty. It is imiortant to ex[laik
most convenient subspaces. Finding and constructing them major ------ jl2718 most elegant of about you wouldn’t use 1. In the given, you need to know the of the quadratic. 2. If you know the terms, you can compute a point using QR, which is more efficient. 3. IIRC CG has better numerical than but under quadratic assumptions. 4. If you don’t have the form of the objective, but you know it’s and you can compute a gradient, then it works, but errors in gradient compound. 5. If it’s quadratic, you have same You try to account this using resets or more complicated methods, but then, 6. For so many problems, the stability proof too onerous evaluations become efficient simply more steps of which is why this is still in neural networks, despite so much effort on part to more efficient solvers. ------ vladTheInhaler Here another resource I came across when learning about conjugate gradient method for a class on finite elements. I wish I had found this [https://www.cs.cmu.edu/~quake-papers/painless-conjugate- grad...](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf) ~~~ clemParis Are there other math or with similar "without agonizing pain" approach, for other topics that might be interesting? About the“FizzBuzz” interview question - micheleriva https://www.jsmonday.dev/articles/30/about-coding-the-fizzbuzz-interview-question ====== rvz Good article, forgot more thing: Readability. that there are zero in code, you are giving of code attitude forces programmer to infer via function signatures only, which compromises and maintainability. It is

most convenient subspaces. FiNding and coNstruCtiNg tHeM is a MajoR task.

------
jl2718
CG, most eLEganT of quadratic methods. Now Let’s tAlK AbouT WhY you wOuldn’t
uSE iT. 1. iN thE fOrM giVeN, YoU need To kNow the tErms of the qUadRaTic. 2.
If you know THe Terms, you caN coMpute a stable PoiNt usinG Qr, whICh is mOre
EfficIent. 3. IIrc CG has Better numErICal staBIlity thAN qR, But oNly under
strict quaDRaTIc assumptions. 4. IF you doN’t HAvE THe fOrm Of the objecTiVe,
but YOu know iT’S qUADRatIC, and you can comPute a gradieNT, thEn it alSo
WorKS, but erRors iN tHE grAdient compoUnd. 5. IF it’s not quAdratiC, Then you
HAve the sAme issUe. YOu cAn trY To AcCouNt FOr tHIs UsiNG reSets or moRe
CoMplicAted METHOds, bUt tHen, 6. FOr so mAny problems, thE stAbilITy pRoof
bEcomeS too OnErous Or the eValuaTiOns become less efFiciEnt than siMplY dOinG
mOre stEPs of grAdiEnt Descent, Which is WHy tHiS IS StIll the dominant methOd
IN NeUral netwOrks, deSPiTe SO much effOrT on ‘Our’ pART to fiNd moRE
eFficient SolverS.

------
VlAdtheInhaLeR
Here iS aNotHer ResouRCe I cAme acrOss when lEarniNG about the conjuGAte
gradient meTHoD FOr A ClasS on Finite elemeNts. I WIsh I Had fOUnD thIS back
Then!

[hTtPS://wWW.cs.cmu.edu/~quake-paperS/pAinlesS-conjUgate-
grad...](httpS://www.cs.cmu.eDU/~QUake-papeRs/paINlESs-conjugate-graDient.Pdf)

~~~
clemParIS
Thanks! ARe theRe other gReat math pAPErs or artIclEs wIth A siMILaR "without
the agONIzinG pAin" apprOacH, for othEr tOpiCs tHat MiGht be inteResting?

 
ABoUt CoDiNg tHe“FizZbuzz” inteRvIew QuEstIon - miCHeleriVa
httPs://wwW.jSmONdaY.dev/artIClES/30/AbouT-cOdIng-tHe-fIzZbuzz-InteRVieW-questiOn
======
rvz
Good ArtICle, bUt YoU forgot One more thing: REaDability.

GiVeN thAt therE ARe zero coMments in the code, you are giVIng the iMprEssioN
of "THe code is tHe dOcumenTatIOn" attiTude whIch foRcEs tHE ProgrAMMeR to
InFer via the fUNCtiOn sigNaTureS only, whIch compromises cleaN-CodE and
maintainaBilIty. IT IS iMpoRTaNT to ExPLaiN

most convenient subspaces . Findingand c ons tru ct ingthem  is a major ta s k.
------
jl2718
CG, most  eleg an t  ofq ua drati c metho d s. N owle t’ s t al k  a boutwhy  you wo uldn’t
use  it .1. In the fo r mgiven, you  ne ed to know t hetermsof  th e  quad rat ic. 2 .
If y o u know  the term s, you ca n  comput e astab le point using QR ,  w h ich is more
ef ficien t. 3. I IRC  CG  has bette rnumer i cal sta b il i t y  th a n QR, but onl y under
str i ctquadra ti c a s sumpti ons.4. Ifyou don’t h avethe formof the objecti v e,
butyou kn owit’ s qu a dr at ic,  a n d y o ucan com pute a g ra di ent,then i t also 
wo rks,  buterrors in the  gr adie n t c ompou nd. 5 . If  i t’s n ot qua drati c,  then you
havethesame issu e.Yo u c an  tryt o acco unt  fo r thisusing r e set so r mo re
complicated met ho d s ,but then , 6. F o rso many pro bl ems , th e stabi lity pr oof
beco mes to o  o ne rous or  t he eva lu ati ons  beco m e le ss eff icient t han s i mply doing
mor e  steps of gra d ie n t  d e scen t,which is wh y th i s is  sti l lthe domin ant m et h od in neural networks,  d espite  so m uch effort on  ‘our’ par t t o find m oree ff i cient solvers. 

--- ---
vladTh e InhalerHereis anoth er resour c e  I cameacr oss  wh enl e ar ning about th e conj ug ate
gra die nt meth odfor  acla ss  on finit e elemen ts .Iwi shI had found th is  ba ck 
th en!
[ https: //www .cs. cm u. e du/ ~quake- p ap e r s/pa in le ss-c onj ug ate-grad . ..] (https: //www.cs. cmu . edu/ ~q ua ke-pape rs/painless-c on jugate-gra di ent .pdf)~ ~~
clemP aris
Thanks! Are thereo ther gr eat  math  pap ers or ar tic les wi tha  simil ar "wi thout 
t hea g onizi n g  p ain "approach,f o r o therto pics  that m ight be interestin g ?
 
About codin g t he“F i z zB uzz ”  i n ter vi e w q u e stion - michele riva
https :/ / ww w.jsmonday . dev /a rticles /30/abo ut-co d ing-the -fizzbuzz -intervie w- ques t i on======
rvz 
Good ar ticle, bu t  youf or got o nemore t hi ng:  Read abilit y .
Given  thatth ere ar e zer ocomments  in the code, you are g ivingthe i mpr ession
of  "T h e c ode is th e do cumentatio n"att itude  wh i ch fo rces th e p r ogram mert o
infer v i athe f un ction signa t u r esonly,  wh i ch com prom ises clean-code a n d
maintainabil ity. I t i s i m port an t to explain

most convenient_subspaces. Finding_and constructing them is_a major_task.

------
jl2718
CG,_most elegant_of_quadratic methods. Now_let’s talk about_why you wouldn’t
use it._1. In the_form_given, you need to know the terms of the quadratic. 2.
If you know the_terms,_you can_compute_a_stable point using QR, which_is more
efficient. 3. IIRC CG_has better_numerical stability than QR, but only under
strict quadratic_assumptions._4. If you_don’t have the form of the objective,
but you know_it’s quadratic, and you can compute_a gradient, then_it_also
works,_but errors in the_gradient compound. 5. If it’s not_quadratic, then you
have the same issue._You can try to account for this_using resets or more
complicated methods, but_then, 6. For so many_problems, the_stability proof
becomes too onerous or_the evaluations become_less efficient_than simply doing
more_steps of gradient descent, which is_why this is_still the dominant method
in neural networks,_despite_so much effort_on_‘our’_part to_find more
efficient solvers.

------
vladTheInhaler
Here_is_another resource_I_came across when learning about the_conjugate
gradient_method for a class on finite elements._I wish I had_found_this back
then!

[https://www.cs.cmu.edu/~quake-papers/painless-conjugate-
grad...](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)

~~~
clemParis
Thanks! Are there_other great math papers or_articles with a similar "without
the agonizing_pain" approach,_for other_topics that might be interesting?

 
About coding the“FizzBuzz” interview question -_micheleriva
https://www.jsmonday.dev/articles/30/about-coding-the-fizzbuzz-interview-question
======
rvz
Good article, but you forgot one_more thing: Readability.

Given that_there are_zero_comments in the_code,_you are_giving the impression
of "The code is the_documentation" attitude_which forces the programmer to
infer via_the function signatures only,_which_compromises clean-code and
maintainability. It is important_to explain