OpenLLM-France/wikimedia huggingface dataset:
# 2003 European Athletics U23 Championships – Women's 10,000 metres

The women's 10,000 metres event at the 2003 European Athletics U23 Championships was held in Bydgoszcz, Poland, at Zawisza Stadion on 19 July.

## Medalists

| Gold | Krisztina Papp Hungary |
| Silver | Valentina Levushkina Russia |
| Bronze | Louise Damen United Kingdom |

## Results
### Final

19 July
| Rank | Name | Nationality | Time |
| | Krisztina Papp | Hungary | 33:23.02 |
| | Valentina Levushkina | Russia | 33:28.73 |
| | Louise Damen | United Kingdom | 33:29.82 |
| 4 | Iryna Kunakhavets | Belarus | 34:02.63 |
| 5 | Collette Fagan | United Kingdom | 34:08.93 |
| 6 | Oksana Sklyarenko | Ukraine | 34:12.66 |
| 7 | Nicole Güldemeister | Germany | 34:16.71 |
| 8 | Anna Rahm | Sweden | 34:18.46 |
| 9 | Michaela Schedler | Germany | 34:22.36 |
| 10 | Nathalie De Vos | Belgium | 34:43.11 |
| 11 | Rosana Fernández | Spain | 34:46.55 |
| 12 | Nina Thysk Sørensen | Denmark | 35:08.42 |
| 13 | Minna Myllykoski | Finland | 35:20.33 |
| 14 | Karolina Jarzyńska | Poland | 35:20.92 |

## Participation

According to an unofficial count, 14 athletes from 12 countries participated in the event.
* Belarus (1)
* Belgium (1)
* Denmark (1)
* Finland (1)
* Germany (2)
* Hungary (1)
* Poland (1)
* Russia (1)
* Spain (1)
* Sweden (1)
* Ukraine (1)
* United Kingdom (2)
# Gorihorn

The Gorihorn (also known as Isentällispitz) is a mountain of the Silvretta Alps, located north of the Flüela Pass in the Swiss canton of Graubünden.
# Anbulla Malare

Anbulla Malare (transl. Dear flower) is a 1984 Indian Tamil-language film directed by B. R. Ravishankar and produced by V. V. Babu. The film stars Vijay Menon and Shanthi Krishna. It was released on 11 May 1984.

## Cast

* Vijay Menon
* Shanthi Krishna
* Baby Anju

## Soundtrack

The music was composed by Ilaiyaraaja.
| Song | Singers | Lyrics |
| Alai Meethu Thadumaruthe | S. P. Balasubrahmanyam, Vani Jairam | Vairamuthu |
| Enna Venum | Grubb Singh, Saibaba | Gangai Amaran |
| Kadhal Thegangal | P. Susheela, S. P. Balasubrahmanyam | Vairamuthu |
| Paathingala En Udan Pirappe | S. P. Balasubrahmanyam | Gangai Amaran |
| Thaaye Thaaye Dharmam | S. P. Balasubrahmanyam | Vairamuthu |
| Thegam Pon Thegam | S. Janaki | Vairamuthu |
# 2013 Copa San Juan Gobierno – Doubles

Martín Alund and Horacio Zeballos were the defending champions but Zeballos chose not to compete. Alund partnered with Facundo Bagnis and lost in the final to compatriots Guillermo Durán and Máximo González 6–3, 6–0.

## Seeds

* Martín Alund / Facundo Bagnis (final)
* Guido Andreozzi / Eduardo Schwank (first round)
* Renzo Olivo / Marco Trungelliti (semifinals)
* Andrey Kuznetsov / Rubén Ramírez Hidalgo (withdrew)

## Draw
### Key

* Q = Qualifier
* WC = Wild card
* LL = Lucky loser
* Alt = Alternate
* SE = Special exempt
* PR = Protected ranking
* ITF = ITF entry
* JE = Junior exempt
* w/o = Walkover
* r = Retired
* d = Defaulted
* SR = Special ranking

### Draw

| First round | First round | First round | First round | First round | Quarterfinals | Quarterfinals | Quarterfinals | Quarterfinals | Semifinals | Semifinals | Semifinals | Semifinals | Semifinals | Final | Final | Final | Final |
| 1 | M Alund F Bagnis | 6 | 6 | | | | | | | | | | | | | | |
| WC | Francisco Bahamonde Facundo Jofre | 2 | 0 | | 1 | M Alund F Bagnis | | | | | | | | | | | |
| WC | Facundo Alvo P Cachin | w.o | | | | M Estévez M Martinez | w.o | | | | | | | | | | |
| | Maximiliano Estévez Mateo Martinez | | | | | | | | 1 | M Alund F Bagnis | 6 | 6$^4$ | [10] | | | | |
| Alt | Sebastian Bettiol G Villanueva | 4 | 4 | | | | | | | C Garin E Gómez | 3 | 7$^7$ | [6] | | | | |
| | C Garin E Gómez | 6 | 6 | | | C Garin E Gómez | 6 | 7 | | | | | | | | | |
| | Raul Guardia Guillermo Riccitelli | 1 | 0 | | | GA Hidalgo S Travaglia | 4 | 5 | | | | | | | | | |
| | Gabriel Alejandro Hidalgo S Travaglia | 6 | 6 | | | | | | | | | | | 1 | M Alund F Bagnis | 3 | 0 |
| | P Heras A Molteni | 3 | 7 | [7] | | | | | | | | | | | G Durán M González | 6 | 6 |
| | G Lama JI Londero | 6 | 5 | [10] | | G Lama JI Londero | 2 | 4 | | | | | | | | | |
| | T Lipovšek Puches Joaquin Monteferrario | 4 | 6$^4$ | | 3 | R Olivo M Trungelliti | 6 | 6 | | | | | | | | | |
| 3 | R Olivo M Trungelliti | 6 | 7$^7$ | | | | | | 3 | R Olivo M Trungelliti | 1 | 4 | | | | | |
| | A Collarini D Schwartzman | 6 | 2 | [7] | | | | | | G Durán M González | 6 | 6 | | | | | |
| PR | P Galdón Laurent Rochette | 4 | 6 | [10] | PR | P Galdón L Rochette | w.o | | | | | | | | | | |
| | G Durán M González | 6 | 6 | | | G Durán M González | | | | | | | | | | | |
| 2 | G Andreozzi E Schwank | 3 | 2 | | | | | | | | | | | | | | |
# Erchenbald

Erchenbald or Archembald was a mesne lord listed in the Domesday Book of 1086 as a tenant of nine manors in Devon and Cornwall, England. He is believed to be the first English ancestor of the prominent Fleming family.

## Landholdings

The Domesday book records that Erchenbald held three manors in Cornwall and six in Devon, all as tenant of Robert, Count of Mortain, who was a half-brother of William the Conqueror and held over one hundred west country manors as tenant-in-chief.
Erchenbald's landholdings recorded in the Domesday Book are as follows. In Cornwall:
* Brea, Cornwall (in Connerton Hundred)
* Avalde, Cornwall (in Fawton Hundred)
* Bodbrane, Cornwall (in Fawton Hundred)
In Devon:
* Culleigh, in the parish of Frithelstock in Shebbear hundred, Devon;
* Alverdiscott, in Fremington Hundred, Devon;
* Bratton, in Braunton Hundred, Devon, today known as Bratton Fleming;
* Croyde, in the parish of Georgeham, in Braunton Hundred, Devon
* Hele, Devon (probably in Meeth parish)
* Stockleigh, Devon (Meeth parish, Shebbear Hundred)
He was also recorded as holding livestock (five cattle & eight sheep) in the manor of Weare (Giffard), Devon, which was held from Robert Count of Mortain by Roald Dubbed.

## Fleming family

Erchenbald is assumed to be the first English ancestor of the family surnamed "Fleming", of Bratton Fleming. He came to England during the reign of William the Conqueror (1066-1087) and was a follower of that king's uterine half-brother Robert, Count of Mortain. He was succeeded by his son, Stephen (fl. 1145), whose son, "Erchenbald son of Stephen" occurs as holder of several knight's fees in Devon and Cornwall in the 1166 Liber Niger ("Return of the Barons"). He went to Ireland with Henry II in 1171 and participated in Hugh de Lacy's plantation of the Kingdom of Mide. Succeeding Flemings were Stephen, died c. 1213 – 1214 and Baldwin, died 1260.
The lands of Robert, Count of Mortain, became the core holdings of the feudal barony of Launceston, in Cornwall, and the Fleming family continued to hold most of their manors from that barony, as can be seen from entries in the Book of Fees (c.1302) – for example, Baldwin le Flemeng is listed as holding lands in Crideho (Croyde) and also in Bratton' cum membris ("with its member (estates)"), both by then fees held from the feudal barony of Launceston. Baldwin also held Alverdiscott, and held Benton and Haxton, from the feudal barons of Bradninch.
A later descendant, Simon Fleming (died 1370) became the first Baron Slane.
# Giuseppina Princi

Giuseppina Princi (born 27 September 1972) is an Italian politician of Forza Italia who was elected member of the European Parliament in 2024. She served as vice president of Calabria under Roberto Occhiuto until her election.
# Bakken

Bakken may refer to:

## People

* Bakken (surname), list of people with this name

## Places

* Bakken, Agder, a village in Iveland municipality, Agder county, Norway
* The Bakken, a medical electricity museum in Minneapolis, Minnesota, US
* Dyrehavsbakken, a Danish amusement park referred to informally as Bakken
* Bakken formation, a rock unit with producible reserves of oil in North America
* Bakken pipeline, an oil pipeline in the US

## Other

* Bakken Air, an airline based in Bismarck, North Dakota
* Bakken Bears, a Danish professional basketball club
# Grand National Handicap

The Grand National Handicap was an American Thoroughbred race horse first run in 1866 at the newly built Jerome Park Racetrack in Fordham, New York. Open to horses age three and older, the race was contested on dirt at a distance of 2+1⁄4 miles from inception through 1884. In the late 1880s, there was a growing shortage of handicap horses and track officials shortened the race in an attempt to draw more entrants. In 1885 it was run at 1+3⁄4 miles, and for its final four years from 1886 through 1889 at 1+1⁄2 miles.
Because Jerome Park Racetrack had a number of viability problems and did not reopen in 1890, the last time the Grand National Handicap was run was in 1889.
In winning the final two editions of the Grand National Handicap in 1888 and 1889, Raceland defeated the future U.S. Racing Hall of Fame filly, Firenze.

## Winners

| Year | Winner | Age | Jockey | Traner | style=Owner | Dist. (Miles) | Time |
| 1889 | Raceland | 4 | | Frank McCabe | Michael F. Dwyer | 11⁄2 m | 2:39.25 |
| 1888 | Raceland | 3 | | Frank McCabe | Michael F. Dwyer | 11⁄2 m | 2:39.75 |
| 1887 | Linden | 4 | | | | 11⁄2 m | 2:42.75 |
| 1886 | Wickham | 4 | | | | 11⁄2 m | 2:40.00 |
| 1885 | Bob M | 4 | | | | 13⁄4 m | 3:12.00 |
| 1884 | Drake Carter | 4 | | | | 21⁄4 m | 4:11.50 |
| 1883 | George Kinney | 3 | | | | 21⁄4 m | 4:11.00 |
| 1882 | Girofle | 5 | | | | 21⁄4 m | 4:11.00 |
| 1881 | Monitor | 5 | | | | 21⁄4 m | 4:07.75 |
| 1880 | Uncas | 4 | | | | 21⁄4 m | 4:05.25 |
| 1879 | General Philips | 5 | | | | 21⁄4 m | 4:07.50 |
| 1878 | Lou Lanier | 3 | Harry Blaylock | | | 21⁄4 m | 4:06.75 |
| 1877 | Tom Ochiltree | 5 | | | | 21⁄4 m | 4:18.50 |
| 1876 | Vigil | 3 | | David McDaniel | David McDaniel | 21⁄4 m | 4:11.00 |
| 1875 | Aaron Pennington | 4 | | | | 21⁄4 m | 4:15.75 |
| 1874 | Mate | 5 | | | | 21⁄4 m | 4:13.75 |
| 1873 | Preakness | 6 | | | | 21⁄4 m | 4:08.75 |
| 1872 | Tubman | 4 | | | | 21⁄4 m | 4:10.75 |
| 1871 | Monarchist | 3 | | | | 21⁄4 m | 4:09.00 |
| 1870 | Niagara | 4 | | | | 21⁄4 m | 4:09.25 |
| 1869 | La Polka | 4 | | | | 21⁄4 m | 4:18.25 |
| 1868 | De Courcey | 4 | | | | 21⁄4 m | 4:11.50 |
| 1867 | Local | 4 | | | | 23⁄4 m | 5:09.00 |
| 1866 | Kentucky | 5 | | A. Jackson Minor | Annieswood Stable (Belmont/Hunter/Jerome/Cameron/Travers) | 23⁄4 m | 5:04.00 |
# Hammer the Hammer

"Hammer the Hammer" was released as a stand-alone single by Australian indie group The Go-Betweens. It was released as a 7" vinyl record on the Missing Link Records label in Australia in June 1982 and by Rough Trade Records in the United Kingdom in July, with "By Chance" as the B-side. Forster considered that "By Chance" was a personal break-through for him. Pitchfork Media describes "By Chance" as sounding "more than a bit like the early Smiths.

## Details

According to music journalist Clinton Walker "Hammer the Hammer" was about McLennan's growing taste for narcotics encouraged by a proximity to the Birthday Party. McLennan however denied that the song was about drugs and in the liner notes for the band's compilation album, 1978-1990, he describes it as being "an incomplete meditation on loneliness and violence, sometimes mistakenly thought to be about drugs".
Forster described the song as, "Grant's first great pop tune. An urgent, melodic verse, a foot to the floor chorus - its lyric just the repeated title. Perfect. From his earliest songs I found his lyrics surprisingly oblique and melancholic."
The band recorded the two songs at Armstrong's Audio Visual (A.A.V.) Studios in Melbourne, at the same time as The Birthday Party was recording Junkyard. It was during these sessions that the two groups decided to collaborate on a song. The result, "After the Fireworks", was a Forster/McLennan joint composition with the lyrics by Nick Cave. It was subsequently released by on Au Go Go Records (ANDA-22) under the name Tuff Monks.

## Reception

Reviewed in NME at the time of release, it was described as, "Miscreant pop music attempting to disgrace its fealty to any number of sources. It seems to stumble when a stride is called for and winds up notating needless obscurities. Vacancy trussed up as abstraction is not the stuff of success, in any sense."
The Guardian describes the song as an "odd, punkish sort of folk rock, deceptively primitive and sometimes rattlingly suggestive of the Velvet Underground."

## Release history

| Date | Region | Label | Format | Catalogue |
| June 1982 | Australia | Missing Link | 7" vinyl | MISS 33 |
| July 1982 | United Kingdom | Rough Trade | 7" vinyl | RT 108 |

## Credits
### The Go-Betweens

* Robert Forster – vocals, rhythm guitar
* Grant McLennan – vocals, bass guitar, lead guitar
* Lindy Morrison – drums, vocals

### Production

* Producer, Engineer — Tony Cohen
* Producer — The Go-Betweens
# Governor of Amasya

The Governor of Amasya (Turkish: Amasya Valiliği) is the bureaucratic state official responsible for both national government and state affairs in the Province of Amasya. Similar to the Governors of the 80 other Provinces of Turkey, the Governor of Amasya is appointed by the Government of Turkey and is responsible for the implementation of government legislation within Amasya. The Governor is also the most senior commander of both the Amasya provincial police force and the Amasya Gendarmerie.

## Appointment

The Governor of Amasya is appointed by the President of Turkey, who confirms the appointment after recommendation from the Turkish Government. The Ministry of the Interior first considers and puts forward possible candidates for approval by the cabinet. The Governor of Amasya is therefore not a directly elected position and instead functions as the most senior civil servant in the Province of Amasya.

### Term limits

The Governor is not limited by any term limits and does not serve for a set length of time. Instead, the Governor serves at the pleasure of the Government, which can appoint or reposition the Governor whenever it sees fit. Such decisions are again made by the cabinet of Turkey. The Governor of Amasya, as a civil servant, may not have any close connections or prior experience in Amasya Province. It is not unusual for Governors to alternate between several different Provinces during their bureaucratic career.

## Functions

The Governor of Amasya has both bureaucratic functions and influence over local government. The main role of the Governor is to oversee the implementation of decisions by government ministries, constitutional requirements and legislation passed by Grand National Assembly within the provincial borders. The Governor also has the power to reassign, remove or appoint officials a certain number of public offices and has the right to alter the role of certain public institutions if they see fit. Governors are also the most senior public official within the Province, meaning that they preside over any public ceremonies or provincial celebrations being held due to a national holiday. As the commander of the provincial police and Gendarmerie forces, the Governor can also take decisions designed to limit civil disobedience and preserve public order. Although mayors of municipalities and councillors are elected during local elections, the Governor has the right to re-organise or to inspect the proceedings of local government despite being an unelected position.
# Follansbee (surname)

Follansbee is a surname. Notable people with the surname include:
* Clyde Follansbee (1902–1948), American politician
* Edward Follansbee Noyes (1832–1890), American politician
* Elizabeth Follansbee (1839–1917), American physician and professor
# Erica Sanders

Erica Niamh Sanders (born 18 May 1997) is an English field hockey player who plays as a forward for Dutch club hdm and the England and Great Britain national teams.

## Club careers

She plays club hockey in the Dutch Hoofdklasse for hdm.
Sanders has also played for Surbiton, University of Birmingham and Beeston.
# Gisburg

Gisburg (born Gisburg Smialek, 1966) is an Austrian composer, singer, and music editor for film.

## Biography

Gisburg born in Salzburg, Austria. She began studying modern music theater with Dieter Schnebel and was touring around the world as a concert singer with his vocal group Die Maulwerker. She attended the Berlin University as a guest student for composition and modern music theatre with Prof. Dieter Schnebel and Prof. Witold Szalonek and for visual arts with Eva Maria Schön. She moved to New York City in 1992 and performed around the Knitting factory and Roulette scene. She recorded albums for Tzadik. and GP music. She was a member of the Chinese Hai-Tien choir with Mrs. Pi-Chu Hsiao for 6 years, and recorded with Gary Lucas Chinese pop music of the 1930s and 1950s.
She scored several music scores for films and works as a music editor in NYC.
Besides this she is the co-founder of the Filmette Film Festival , with Drew Pisarra and Loui Terrier. Filmette is a Film Festival which champions films outside the usual Festival time constraints.
# 1990 Gent–Wevelgem

The 1990 Gent–Wevelgem was the 52nd edition of the Gent–Wevelgem cycle race and was held on 4 April 1990. The race started in Ghent and finished in Wevelgem. The race was won by Herman Frison of the Histor–Sigma team.

## General classification

| Rank | Rider | Team | Time |
| 1 | Herman Frison (BEL) | Histor–Sigma | 4h 59' 00" |
| 2 | Johan Museeuw (BEL) | Lotto–Superclub | + 0" |
| 3 | Franco Ballerini (ITA) | Del Tongo | + 0" |
| 4 | Frans Maassen (NED) | Buckler–Colnago–Decca | + 0" |
| 5 | Jean-Marie Wampers (BEL) | Panasonic–Sportlife | + 2" |
| 6 | Brian Holm (DEN) | Histor–Sigma | + 4" |
| 7 | Olaf Ludwig (FRG) | Panasonic–Sportlife | + 4" |
| 8 | Dimitri Konyshev (URS) | Alfa Lum | + 4" |
| 9 | Steve Bauer (CAN) | 7-Eleven | + 4" |
| 10 | Rudy Dhaenens (BEL) | PDM–Concorde–Ultima | + 4" |
# Ballard, Queensland

Ballard is a rural locality in the Lockyer Valley Region, Queensland, Australia. In the 2021 census, Ballard had a population of 167 people.

## Geography

Ballard is located 11 kilometres (7 mi) east from the Toowoomba city centre. Murphys Creek Road passes through the northwest corner.

## History

The locality, historically known as Ballaroo, is named for Robert Ballard, a railway engineer for Peto, Brassey and Betts who oversaw the construction of the main range section of the Ipswich–Toowoomba railway.
In December 1885, "The Highfields Estate" made up of 147 allotments was advertised for sale by Arthur Martin & Co. Despite the use of the Highfields name, the estate is not within present day Highfields but is predominantly within present day Ballard with small areas in Blue Mountain Heights and Murphys Creek. A map advertising the land sale illustrates the location of the estate in proximity to the "S & W Railway line" and the Highfields railway station (now known as Spring Bluff railway station) and shows town allotments in the area of the intersection of Valley View Road and Hanleys Road (27°29′23″S 151°58′06″E﻿ / ﻿27.4897°S 151.9682°E﻿ / -27.4897; 151.9682﻿ (Town of Ballard)). The map describes the estate as the "Sanatorium and Garden of Queensland".

## Demographics

At the 2006 census, tBallard had a population of 355 people.
In the 2016 census, Ballard had a population of 151 people.
In the 2021 census, Ballard had a population of 167 people.

## Heritage listings

Ballard has a number of heritage-listed sites, including:
* 6 kilometres (3.7 mi) north of Toowoomba: Swansons Rail Bridge

## Education

There are no schools in Ballard. The nearest government primary schools are Harlaxton State School in neighbouring Harlaxton to the south, Withcott State School in neighbouring Withcott to the east, and Murphys Creek State School in neighbouring Murphys Creek to the north-west. The nearest government secondary schools are Toowoomba State High School in neighbouring Mount Lofty to the south-east and Centenary Heights State High School in Centenary Heights to the south.
# Ballard, West Virginia

Ballard is an unincorporated community in Monroe County, West Virginia, United States. Ballard is located on West Virginia Route 12, north of Peterstown. Ballard has a post office with ZIP code 24918.
The community has the name of Clayton A. Ballard, an early storekeeper.
Ballard is home to Ballard Christian School, which was formed in 1977. The closest high school is James Monroe High, which serves all of Monroe County. The town is also home to a variety of churches and several small business.
The average temperature is approximately 51 °F, lower than the West Virginia average temperature of 53 °F.
# Ballard, Missouri

Ballard is an unincorporated community in northeast Bates County, in the U.S. state of Missouri and is part of the Kansas City metropolitan area.
The community is located on Missouri Route 18 approximately four miles west of the Bates-Henry county line. Adrian on U.S. Route 71 is about ten miles to the west. Tributaries of North Deepwater Creek drain the area to the south.

## History

Ballard was named for Hon. J. N. Ballard, a county judge and afterward state senator. A post office was briefly located in Ballard before it was replaced by Rural Free Delivery routes. A 1918 Bates County history reported that the mercantile store in Ballard had a "nice, clean stock of merchandise".
Ballard R-2 School District provides education for the community.
# Generalized Wiener filter

The Wiener filter as originally proposed by Norbert Wiener is a signal processing filter which uses knowledge of the statistical properties of both the signal and the noise to reconstruct an optimal estimate of the signal from a noisy one-dimensional time-ordered data stream. The generalized Wiener filter generalizes the same idea beyond the domain of one-dimensional time-ordered signal processing, with two-dimensional image processing being the most common application.

## Description

Consider a data vector $d$ which is the sum of independent signal and noise vectors $d=s+n$ with zero mean and covariances $\langle ss^{T}\rangle =S$ and $\langle nn^{T}\rangle =N$. The generalized Wiener Filter is the linear operator $G$ which minimizes the expected residual between the estimated signal and the true signal, $e=\langle (Gd-s)^{T}(Gd-s)\rangle$. The $G$ that minimizes this is $G=S(S+N)^{-1}$, resulting in the Wiener estimator ${\hat {s}}=S(S+N)^{-1}d$. In the case of Gaussian distributed signal and noise, this estimator is also the maximum a posteriori estimator.
The generalized Wiener filter approaches 1 for signal-dominated parts of the data, and S/N for noise-dominated parts.
An often-seen variant expresses the filter in terms of inverse covariances. This is mathematically equivalent, but avoids excessive loss of numerical precision in the presence of high-variance modes. In this formulation, the generalized Wiener filter becomes $G=(S^{-1}+N^{-1})^{-1}N^{-1}$ using the identity $A^{-1}+B^{-1}=A^{-1}(A+B)B^{-1}$.

## An example

The cosmic microwave background (CMB) is a homogeneous and isotropic random field, and its covariance is therefore diagonal in a spherical harmonics basis. Any given observation of the CMB will be noisy, with the noise typically having different statistical properties than the CMB. It could for example be uncorrelated in pixel space. The generalized Wiener filter exploits this difference in behavior to isolate as much as possible of the signal from the noise.
The Wiener-filtered estimate of the signal (the CMB in this case) ${\hat {s}}=S(S+N)^{-1}d$ requires the inversion of the usually huge matrix $S+N$. If S and N were diagonal in the same basis this would be trivial, but often, as here, that isn't the case. The solution must in these cases be found by solving the equivalent equation $(S+N)S^{-1}{\hat {s}}=d$, for example via conjugate gradients iteration. In this case all the multiplications can be performed in the appropriate basis for each matrix, avoiding the need to store or invert more than their diagonal. The result can be seen in the figure.